Periodic Partial Differential Operators and Their Applications I. Elliptic Equations. The Main Structures, in preparation.
Periodic Partial Differential Operators and Their Applications II. Generalizations and Applications, in preparation.
Eclectic Notes on Harmonic Analysis, in preparation.
(with M. Agranovsky and Linh Nguyen) Spherical Mean Operators and their Applications, in preparation.
Editor (with A. Golberg and D. Shoikhet)
Harmonic Analysis and Partial Differential Equations: In Honor of Vladimir Maz'ya/i>, Birkhauser, 2023.
(with Minh Kha) Liouville-Riemann-Roch Theorems on
Abelian Coverings, Springer, 2021.
(Editor, with E. Semenov) Functional Analysis and Geometry. Selim Grigorievich Krein
Centennial, CONM vol. 733, AMS 2019. 
(Editor, with E. Semenov)
Differential Equations, Mathematical Physics, and Applications. Selim Grigorievich Krein Centennial,
CONM vol. 734, AMS 2019. 
The Radon Transform and Medical Imaging, SIAM 2014.
(with G. Berkolaiko)
Introduction to Quantum Graphs, Mathematical Surveys and Monographs, V. 186 AMS, 2013.
Floquet Theory For Partial
Differential Equations, Birkhauser Verlag, Basel, 1993. 
(Editor, with G. Bal, D. Finch, J. Schotland,
P. Stefanov, and G. Uhlmann) Tomography and Inverse Transport Theory,
Contemp. Mathematics, v. 559, AMS 2011. 
(Editor, with M. Braverman, L.
Friedlander, T. Kappeler, P. Topalov, and J. Weitsman) Spectral theory and geometric analysis,
Contemporary Mathematics v. 353, AMS 2011, 213pp. 
(Editor, with P. Exner, J.
Keating, T. Sunada and A. Teplyaev) Analysis on Graphs and its
Applications, Proc. Symp. Pure Math., AMS,2008. 
(Editor, with G. Berkolaiko, R.
Carlson, and S. Fulling) Quantum Graphs and Their Applications,
Contemp. Math., v. 415, American Math. Society, Providence, RI 2006.
(Editor) Waves in Periodic and
Random Media, Contemp. Math. v. 339, American Math. Society,
Providence, RI 2004. 
(Editor, with V. Lin) Voronezh
Winter Mathematical Schools. Dedicated to Selim Krein, American
Math. Society Transl., Ser. 2, v.184, AMS, Providence, RI 1998 
(Editor, with M. Cheney and E.T.
Quinto) Tomography, Impedance Imaging, and Integral Geometry,
Lectures in Appl. Math., vol. 30, American Math. Society, Providence, RI 1994. 
(Editor) Functional Spaces and Equations of Mathematical Physics, Voronezh, USSR, 1988 (in Russian)
(Translator) S. Helgason, Groups
and Geometric Analysis, Moscow, Mir, 1986 (Translation to
Russian from the English edition , Academic Press, 1984). 
(Scientific Editor) S.G. Krein and N.I. Yatskin, Linear
Differential Equations on Manifolds, Voronezh State Univ. Publ.,
1980. 
(see also non-refereed papers and other writing, books and lecture notes for students)
(with L. Kunyansky) Observability for the wave equation and range description for the spherical Radon transform, in preparation.
(with S. Akduman) Open book analogs of quantum graphs (temporary title), in preparation.
(with G. BERKOLAIKO, Y. CANZANI, G. COX, AND J.L. MARZUOLA) STABILITY OF SPECTRAL PARTITIONS WITH CORNERS, in preparation.
Analytic and algebraic properties of dispersion relations (Bloch varieties) and Fermi surfaces. What is known and unknown, J. Math. Phys. 64 (2023), no. 11, Paper No. 113504, 11 pp.
(with L. Kunyansky and F. Terzioglu) TBA, in preparation.
(with G. Berkolaiko) Spectral shift via "lateral" perturbation, J. Spectr. Theory 12 (2022), no. 1, 83–104.
(with J. Taskinen) Dispersion relations and spectra of periodically perforated structures, Pure Appl. Funct. Anal. 7 (2022), no. 2, 721–731.
Three-representation problem in Banach spaces, Complex Analysis and Operator Theory (2021) 15:34, https://doi.org/10.1007/s11785-021-01079-6
Exploring the radon transform and the field of medical imaging. SIAM News 54 (2021), no. 10, 6.
Misterio de dominio nodal, Memorias del Colquio Interinstituticional de Analisis y sus Aplicaciones, Mexico, 2020, pp. 184 -- 191.
(with Weston Baines and Jean Ragusa)
Deep learning for 2D passive source detection in
presence of complex cargo, Inverse Problems 36 (2020) 104001 (23pp). https://doi.org/10.1088/1361-6420/abb51d
(with Ngoc T. Do and F. Sottile)
Generic properties of dispersion relations for discrete periodic operators, J. Math. Physics 61(2020),
Issue 10, https://doi.org/10.1063/5.0018562.
(with James E. Corbin)
Spectra of "fattened" open book type structures, in
The Mathematical Legacy of Victor Lomonosov, De Gruyter 2020, pp. 99 - 108.
DOI: https://doi.org/10.1515/9783110656756
(with Jia Zhao)
Analyticity of the spectrum and Dirichlet-to-Neumann operator technique for quantum graphs,
J. Math. Phys. 60, 093502 (2019); https://doi.org/10.1063/1.5110193.
(with Sergey Lvin) Some binomial formulas
for non-commuting operators, in Functional Analysis and Geometry. Selim Grigorievich Krein Centennial,
Contemporary Mathematics, V. 733, AMS 2019, pp. 197 - 208.
(with David Auckly) On Parseval frames of exponentially decaying composite Wannier functions,
arXiv preprint. Contemporary Mathematics
Volume 717 (2018), 227--240.
https://doi.org/10.1090/conm/717/14451
On a problem concerning affine-invariant points of convex sets,
arXiv:1602.04377. This is English (somewhat updated) version of the Russian language paper A problem about affine-invariant points of convex bodies,
Optimizaciya, Novosibirsk, no.8, 1972, 48--51. (with Minh Kha and A.
Raich) Green's function asymptotics near the internal edges of spectra of periodic elliptic operators: spectral gap interior,
INI preprint. (with L. Kunyansky and Fatma Terzioglu), Compton camera imaging and the cone transform: a brief overview,
Inverse Problems, 34 (2018), 054002 (16pp)
(with Fatma Terzioglu) Inversion of weighted divergent beam and cone
transforms, Inverse Problems and Imaging, Volume 11, No. 6, 2017, 1071--1090.
(with Ngoc T. Do and Beng-Seng Ong) On resonant spectral gap opening in quantum graph networks,
preprint, Functional Analysis and Operator Theory for Quantum Physics,
pp. 213 - 222, European Mathematical Society 2017.
(with Fatma Terzioglu) 3D Image Reconstruction
from Compton camera data, SIAM J. on Imaging Science 9 (2016), No. 4, pp. 1708-1725 .
An overview of periodic elliptic operators,
BULLETIN (New Series) OF THE
AMERICAN MATHEMATICAL SOCIETY,
Volume 53, Number 3, July 2016, Pages 343 414
http://dx.doi.org/10.1090/bull/1528.
Article electronically published on April 6, 2016, arXiv preprint.
(with M. Allmaras, W. Charlton, A. Ciabatti,
Y. Hristova, A. Olson, J. Ragusa)
Passive Detection of Small Low-Emission Sources:
Two-Dimensional Numerical Case Studies, preprint
arXiv:1309.5974,
Nuclear Sci. and Eng. v. 184, no.1, 2016. dx.doi.org/10.13182/NSE15-66 (with O.
Scherzer) Mathematical Methods in Photoacoustic imaging,
Encyclopedia of Applied and Computational Mathematics, Springer Verlag 2015.
(with D. Steinhauer), Stabilizing inverse problems by internal data. II.
Non-local internal data and generic linearized uniqueness (with Ngoc T. Do)
Quantum graph spectra of a graphyne structure, Nanoscale Systems: Mathematical Modeling, Theory
and Applications 2 (2013), 107--123. DOI: 10.2478/nsmmt-2013-0007 (with S. Lvin), Identities
for sin(x) that came from medical imaging, Amer. Math. Monthly 120 (2013), no. 7, 609 - 621.
(with M. Allmaras, D. Darrow,
Y. Hristova, and G. Kanschat)
Detecting small low emission radiating sources, Inverse Problems and Imaging 7 (2013), no. 1, 47-79.
(with D. Steinhauer) Stabilizing inverse problems by internal data,
Inverse Problems 28(2012), no. 8, p.4007, doi:10.1088/0266-5611/28/8/084007 (with G. Berkolaiko
and U. Smilansky) Critical partitions and nodal deficiency of eigenfunctions,
GAFA 2012, DOI: 10.1007/s00039-012-0199-y.
(with G. Berkolaiko) Dependence of
the spectrum of a quantum graph on vertex conditions and edge lengths,
in "Spectral Geometry," Proc. Symp. Pure Math.,
AMS., v. 84, 2012.
(with A. Raich) Green's function
asymptotics near the internal edges of spectra of periodic elliptic
operators. Spectral edge case, Mathematische Nachrichten, 2012, DOI 10.1002/mana201100272.
Mathematics of Hybrid Imaging. A Brief Review, in I. Sabadini and D. Struppa (Editors)
The Mathematical Legacy of Leon Ehrenpreis, Springer, 2012, pp. 183 - 208.
(with X.
Xun, B. Mallick, and R. Carroll)
Bayesian approach
to detection of small low emission sources, Inverse Problems 27 (2011), 115009 (11pp).
(with L. Kunyansky)
2D and 3D
reconstructions in acousto-electric tomography,
Inverse Problems 27 (2011), 055013 (21pp). doi:10.1088/0266-5611/27/5/055013. Featured article.
(with M. Agranovsky) The
support theorem for the single radius spherical mean transform,
Memoirs on Differential Equations and Mathematical Physics 52 (2011), 1-16.
(with L. Kunyansky)
Mathematics of
thermoacoustic and photoacoustic tomography, Chapter 19 in Vol. 1--3 of "Handbook of Mathematical Methods in Imaging", 1688 pp.
Springer, New York, 2015., pp. 1117 1167.
(with P. Exner and B. Winn) On
the location of spectral edges in Z-periodic media,
J. Phys. A: Math. Theor. 43 (2010) 474022.
(with B. Ong) On
guided electromagnetic waves in photonic crystal waveguides, in "Operator Theory and Its Applications: In Memory of
V. B. Lidskii (1924--2008)", Amer. Math. Soc. Transl., v. 231, AMS, Providence, RI, 2010, pp. 99-108.
(with
L. Kunyansky) Synthetic
focusing in ultrasound modulated tomography, Inverse Problems and Imaging, V 4 (2010), Number 4, 665 -- 673.
(with M. Agranovsky and D. Finch)
Range conditions for a
spherical mean transform, Inverse Problems and Imaging, Volume
3, No. 3, 2009, 373-382.
(with M. Agranovsky and L.
Kunyansky) On
reconstruction formulas and algorithms for the thermoacoustic and
photoacoustic tomography, Ch. 8 in L. H. Wang (Editor)
"Photoacoustic imaging and spectroscopy," CRC Press 2009,
pp. 89-101.
(with Y. Xu, L. Wang, G.
Ambartsoumian), Limited view thermoacoustic tomography, Ch. 6 in
L. H. Wang (Editor) "Photoacoustic imaging and spectroscopy,"
CRC Press 2009, pp. 61-73.
Tight
frames of exponentially decaying Wannier functions, J. Phys. A:
Math. Theor. 42 (2009) 025203.? IOP (Inst. of Physics)
Select Paper.
(with Y. Hristova and L.
Nguyen), On
reconstruction and time reversal in thermoacoustic tomography in
homogeneous and non-homogeneous acoustic media, Inverse Problems
24 (2008) 055006, doi:10.1088/0266-5611/24/5/055006.
Quantum
graphs: an introduction and a brief survey, in "Analysis on
Graphs and its Applications", Proc. Symp. Pure. Math., AMS
2008, pp.291 - 314.
(with L. Kunyansky)
Mathematics of
thermoacoustic tomography, European J. Appl. Math., 19
(2008), Issue 02, 191-224
(with S. Fulling and J.
Wilson), Index theorems
for quantum graphs, J. Phys. A: Math. Theor. 40 (2007)
14165-14180.
(with V. Smyshlyaev), Slowing down and transmission of waves in high contrast periodic media via
"non-classical" homogenization, Proc. 8th Int. Conf. on Math. & Numerical Aspects of Wave Propagation, Univ. of Reading, 2007, 200-202.
(with M. Agranovsky) Uniqueness
of reconstruction and an inversion procedure for thermoacoustic and
photoacoustic tomography, Inverse Problems 23 (2007) 2089-2102.
Paper selected by the Editorial Board for the 2007
highlights
(with O. Post) On
the spectra of carbon nano-structures , Comm. Math. Phys. 275
(2007), no. 3, 805-826.
On
integral representations of solutions of periodic elliptic
equations, in "Probability and Mathematical Physics, A
Volume in Honor of Stanislaw Molchanov", D. A. Dawson, V.
Jaksic and B. Vainberg (Editors), CRM Proceedings and Lecture Notes,
v. 42 , AMS, Providence, RI 2007, 323 - 339.
(with Y. Pinchover) Liouville
theorems and spectral edge behavior on abelian coverings of compact
manifolds, Trans. Amer. Math. Soc. 359 (2007), no. 12,
5777-5815.
(with J. Harrison, A. Sobolev, and
B. Winn) On
occurrence of spectral edges for periodic operators inside the
Brillouin zone, J. Phys. A: Math. Theor. 40 (2007) 7597-7618.
(with M. Agranovsky and E. T.
Quinto) Range
descriptions for the spherical mean Radon transform, J. Funct.
Anal. 248(2007), 344-386.
(with B. Vainberg), On
the structure of eigenfunctions corresponding to embedded
eigenvalues of locally perturbed periodic graph operators, Comm.
Math. Phys. 268 (2006), 673-686.
(with G. Ambartsoumian), A
range description for the planar circular Radon transform, SIAM
J. Math. Anal. vol. 38, no. 2, 2006, 681-692 Generalized
Transforms of Radon Type and Their Applications, in G. Olafsson
and E. T. Quinto (Editors), The Radon Transform, Inverse
Problems, and Tomography, Proc. Symp. Appl. Math. v. 63, AMS,
Providence, RI 2006, pp.67 - 91.
(with S. Fulling) Coincidence
of length spectra does not imply isospectrality, Inverse
Problems 21(2005), 1391-1395.
Quantum
graphs II. Some spectral properties of quantum and combinatorial
graphs, J. Phys. A 38 (2005), 4887-4900. (with G. Ambartsoumian) On
the injectivity of the circular Radon transform, Inverse
Problems 21 (2005), 473-485.
On
some spectral problems of mathematical physics, in Partial
Differential Equations and Inverse Problems, C. Conca, R.
Manasevich, G. Uhlmann, and M. S. Vogelius (Editors), Contemp. Math.
v. 362, 2004
(with Y. Xu, L. Wang, and G.
Ambartsoumian) Reconstructions
in limited view thermoacoustic tomography, Medical Physics 31(4)
April 2004, 724-733.
Quantum
graphs I. Some basic structures, Waves in Random media, 14
(2004), S107--S128. (with B. Ong), On
guided waves in photonic crystal waveguides, in Waves in
Periodic and Random Media, Contemp. Math. v. 339, American Math.
Society, Providence, RI 2004, 105-115. (with N. Benchama), An
asymptotic model for wave propagation in thin high cointrast 2D
acoustic media, in Progres in Analysis, H. Begehr, R. Gilbert, and
M. Wong (Editors), v. 1, World. Sci., New Jersey, 2003, 647-650. (with H. Zeng), Asymptotics
of spectra of Neumann Laplacians in thin domains, in Advances in
Differential Equations and Mathematical Physics, Yu. Karpeshina, G.
Stolz, R. Weikard, and Y. Zeng (Editors), Contemporary Mathematics
v.387, AMS 2003, 199-213. Differential and
pseudo-differential operators on graphs as models of mesoscopic
systems, in Analysis and Applications, H. Begehr, R. Gilbert, and M.
W. Wang (Editors), Kluwer Acad. Publ. 2003, 7-30. (with E. T. Quinto) Some problems
of integral geometry arising in tomography, Ch. XI in "The
Universality of the Radon Transform" by L. Ehrenpreis, Oxford
Univ. Press, 2003.
Graph
models of wave propagation in thin structures, Waves in Random
Media 12(2002), no. 4, R1-R24.? Accessed (full text) on
the journal's Web site 291 times in 2002.
(with L. Kunyansky)
Differential operators on graphs and photonic crystals, Adv. Comp.
Math. 16(2002), no. 2-3, 263-290.
(with S. Levendorskii) On
the structure of spectra of periodic elliptic operators, Trans.
AMS 354 (2002), 537-569.
(with H. Zeng), Convergence
of spectra of mesoscopic systems collapsing onto a graph, J.
Math. Anal. Appl. 258(2001), 671-700.
The Mathematics of Photonic
Crystals, Ch. 7 in "Mathematical Modeling in Optical Science",
Gang Bao, Lawrence Cowsar, and Wen Masters (Editors), Frontiers in
Applied Mathematics v. 22, SIAM, 2001, 207 - 272.
(with Y. Pinchover) Integral
representations and Liouville theorems for solutions of periodic
elliptic equations, J. Funct. Anal. 181(2001), 402-446.
(with B. Fridman, K. Lancaster, D.
Ma, M. Mogilevsky, S. Lissianoi, V. Papanicolaou, and I.
Ponomarev), Numerical harmonic analysis on the hyperbolic plane,
Applicable Anal. 76 (2000), 351-362. By an editorial error, the
paper was published with all figures omitted. One can find the
complete PDF preprint with figures at the end here.
(with B. Vainberg) On absence of
embedded eigenvalues for Schr\"{o}dinger operators with
perturbed periodic potentials, Commun. Part. Diff. Equat. 25(2000),
no. 9-10, 1809 - 1826.
(with L. Ehrenpreis and A.
Panchenko), Attenuated Radon transform and F. John's equation.
I. Range conditions, in the Contemporary Mathematics volume
"Analysis, Geometry, Number Theory: The Mathematics of Leon
Ehrenpreis", E. L. Grinberg, S. Berhanu, M. Knopp, G. Mendoza,
and E. T. Quinto, Editors, AMS, 2000.
(with W. Axmann and L.
Kunyansky), Asymptotic methods for thin high contrast 2D PBG
materials, Journal of Lightwave Technology, 17(1999), no.11, 1996-
2007 .
(with S. Levendorskii) On absolute
continuity of spectra of periodic elliptic operators, in
Mathematical Results in Quantum Mechanics, Operator Theory Adv. and
Appl. v. 108, Birkhauser Verlag, Basel 1999, 291-297
(with W. Axmann) An
efficient finite element method for computing spectra of photonic
and acoustic band-gap materials I. Scalar case, J. Comput. Physics
150(1999), 468-481
(with L. Kunyansky)
Spectral properties of high-contrast band-gap materials and
operators on graphs, Experimental Mathematics 8(1999), no.1, 1-28.
(with B. Vainberg) On embedded
eigenvalues of perturbed periodic Schr?dinger operators. Spectral
and scattering theory (Newark, DE, 1997), 67--75, Plenum, New
York,1998.
(with B. Fridman, D. Ma, and V.
Papanicolaou) Solution of the linearized inverse conductivity
problem in the half space via integral geometry, 85-95, in "Voronezh
Winter Mathematical Schools", AMS, Providence, RI, 1998
(with A. Figotin), Spectral
properties of classical waves in high contrast periodic media, SIAM
J. Appl. Math., 58(1998), no.2, 683- 702.
(with A. Figotin) 2D photonic
crystals with cubic structure: asymptotic analysis, in "Wave
propagation in Complex Media", G. Papanicolaou (Editor ), IMA
Volumes in Math. and Appl., Vol. 96, p. 23-30, 1997.
(with M. Agranovsky and C.
Berenstein), Approximation by spherical waves in $L^p$-spaces, J.
Geom. Anal. 6 (1996), no. 3, 365--383.
(with V. Aguilar and L.
Ehrenpreis)Range conditions for the exponential Radon transform, J.
d'Analyse Mathematique, 68(1996), 1-13.
(with A. Figotin) Band-gap
structure of spectra of periodic dielectric and acoustic media. I:
Scalar model, SIAM J. Appl. Math., 56(1996), no.1, 68-88.
(with A. Figotin) Band-gap
structure of spectra of periodic dielectric and acoustic media. II:
2D photonic crystals, SIAM J. Appl. Math. 56(1996), 1561-1620
(with K. Lancaster and L.
Mogilevskaya) On the local tomography, Inverse Problems, 11(1995),
571-589.
(with V. Aguilar) Range
conditions for the multidimensional exponential X-ray transform, in
Inverse Problems 11(1995), 977-982.
(with A. Figotin) Band-gap
structure of spectra of periodic dielectric and acoustic media. II:
2D photonic crystals, preprint #1, January 1995, Math. Dept. UNCC.
On the behavior of Floquet
exponents of a kind of periodic problems, Journal of Differential
Equations 109(1994), no.2, 309-324.
(with I. Shneiberg) Some inversion
formulas in the Single Photon Emission Tomography, Applicable Anal.
53(1994), 221-231.
(with A. Figotin) Band-gap
structure of the spectrum of periodic Maxwell operator, J. Stat.
Phys. 74(1994), no.1/2, 447-458.
On inversion and range
characterization of one transform arising in emission tomography, in
Proceedings of the Conference ``75 years of the Radon transform'',
Internat. Press 1994, p. 240-248.
On positivity problem for Radon
and some related transforms, Contemporary Mathematics 140(1992),
87-95.
(with S. Lvin) The Range of the
Exponential Radon Transform, Soviet Math Dokl, v.42 , no.1, 1991,
p.183-184.
To the Floquet theory of periodic
difference equations , in : ''Geometrical and Algebraical Aspects in
Several Complex Variables'', Cetraro (Italy), June 1989, 203-209,
EditEl, 1991.
(with S. Lvin) Paley-Wiener
theorem for the exponential Radon transform, Acta Applicandae
Mathematicae,no.18, 1990, p. 251-260.
Singularities of the boundary of
the domain of stability in infinite dimensional case, Funkt. Anal. i
Prilozh., v.22, no.3, 1988, p.75-76. English translation in Funct.
Anal. Appl., v.22, no. 3.
Spherical representations of
solutions of invariant differential equations on a Riemannian
symmetric space of noncompact type, Math USSR Izvestiya, v. 27, no.
3, 1986 p. 535-548.
On spectral synthesis in the
spaces of solutions of invariant differential equations, Lecture
Notes in Math., Springer Verlag, v. 1214, 1986, p. 85-100.
On periodic perturbations which
preserve the dispersion relation of a differential operator,
Differencial'nye Uravneniya, v. 22, no. 9, p.1641-1642, 1986.
Translated to English.
(with A. Babichev and others)
Forces which act on a particle in the drum of a
centrifugal-planetary plant, Izvestiya Vusov, Mashinostroyeniye, no.
4, 1986. (In Russian).
(with A. Babichev and others) The
equation of the trajectory of relative motion of a particle during a
centrifugal-planetary processing, ibidem, no. 1, 1986, p.140-143.
(In Russian)
(with A. Babichev and others)
Relative motion of particles in the drum of a centrifugal-planetary
plant, in ''Progressive trimming-strengthening technologies'',
Rostov on Don, 1986, 4 pp. (in Russian).
On the spectral synthesis in the
spaces of solutions of differential equations which are invariant
with respect to transformation groups, in ''Appl of Topology in
Modern Analysis'', Voronezh State Univ. Publ, 1985, p.87-106 (in
Russian).
Representations of solutions of
periodic PDE, Math USSR Izvestiya, v. 21, no. 1, 1983, p. 93-117.
On mean-periodic functions on
symmetric spaces, Funkt Anal i Prilozh, v.16, no.3, 1982, p.68-69.
English transl. in Funct Anal. Appl., v.16, no.3.
Floquet theory for PDE, Russian
Math. Surveys, v.37, no.4,1982, p. 1-60.
Floquet theory for PDE, Doctor of
Science Thesis, Voronezh, 300 pp., 1982 (in Russian).
Representation of solutions of
invariant differential equations on certain symmetric spaces, Soviet
Math Dokl, v.24, no.1, 1981, p. 104-106.
On Floquet theory for parabolic
and elliptic boundary value problems in a cylinder, Soviet Math
Dokl, v.23, 1981, p. 522-525.
Hermite's interpolation problem in
a class of periodic entire functions of a finite order, in ''Linear
operators in function spaces'', Voronezh State Univ. Publ., 1981, p.
63-69 (in Russian).
On the absence of $L_2$-solutions
for some periodic PDEs, Uspehi Mat Nauk, v.35, no.2, 1980, p.211-212
(in Russian). Translated to English.
On Bloch solutions of periodic
PDE, Funkt Anal i Prilozh, v.14, no.1, 1980, p.65-66. English
transl. in Funct Anal Appl, v.14, no.1.
On the Floquet theory for periodic
linear differential equations with deviating arguments, Uspehi Mat
Nauk, v.34, no.3, 1979, p. 201-202 (in Russian). Translated to
English.
On the Floquet representations of
solutions of linear hypoelliptic systems of PDE, Funkt Anal i
Prilozh, v.13, no.1, 1979, p.72. English transl. in Funct Anal and
Appl, v.13, no.1.
Some local properties of the
spectrum of semi-Fredholm operator functions, in ''Operator methods
in differential equations'', Voronezh State Univ. Publ., 1979, p.
49-55 (in Russian).
Representations of solutions of
linear PDE with constant and periodic coefficients, in ''Operator
equations theory'', Voronezh State Univ. Publ., 1979, p. 62-69 (in
Russian).
(with L. Zelenko) On the Floquet
representations of exponentially increasing solutions of elliptic
equations with periodic coefficients, Soviet Math Dokl, v.19, no.2,
1978, p. 506-507.
(with V. Ovchinnikov) On the
problem of lifting of holomorphic functions with values in a Banach
space, in ''Methods of solving of operator equations'', Voronezh
State Univ. Publ., 1978, p. 94-96 (in Russian).
Reconstruction of a continuous
group representation by means of sub-representation and
quotient-representation, Funkt. Anal. i Prilozh., v.10, no.1, 1976,
p.79-80. English transl. in Funct Anal and Appl., v.10, no.1.
(with S. Krein, M. Zaidenberg, and
A. Pankov) Banach bundles and linear operators, Russian Math.
Surveys, v.30, no.5, 1975, p.115-175.
(with A. Pankov) Letter to the
Publisher, Math Sbornik, v.98, no.4 , 1975 (in Russian).
On the lifting of functions with
values in a factor-space of a Banach space, Mat. Issled., Kishinyov,
v.10, no.1, 1975, p.183-193 (in Russian).
Some properties of holomorphic
functions with values in a Banach space, in ''Collection of
scientific papers on applications of functional analysis'', Voronezh
State Univ. Publ., 1975, p.97-101 (in Russian).
(with A. Pankov) Classifying
spaces for the equivariant K-theory, Math. USSR Sbornik, v.24, no.1,
1974, p.31-48
A remark on the homotopic type of
the group of J-unitary operators, Mat. Issled., Kishinyov, v.9,
no.4, 1974, p.170-171 (in Russian)
On complemented subspaces in
spaces with a symmetric basis, Dokl. Akad. Nauk SSSR, v.208, no.5,
1973, p.1027-1030, English transl. in Soviet Math Dokl.
On some properties of
semi-Fredholm operators in a Banach space, Mat. Issled., Kishinyov,
v.8, no.2, 1973, p.80-92 (in Russian).
On the index of Fredholm operators
in a family of Banach spaces, Soviet Math. Dokl., v.13, no.3, 1972,
p.589-592.
(with A. Pankov) On classifying
spaces for the group K p,q G (X), Soviet Math. Dokl., v.13, no.3,
1972, p.789-793.
(with A. Krasnenker) Some
sufficient conditions of the existence of non-homogeneous flows in
networks, Cybernetics, Kiev, no.4, 1972, p.136-138 (in Russian).
Translated to English.
Locally-trivial Banach bundles,
Trudy Inst. Mat. , Voronezh State Univ. Publ., v.5, 1972, p.80-85
(in Russian).
A problem about affine-invariant
points of convex bodies, Optimizaciya, Novosibirsk, no.8, 1972,
p.48-51 (in Russian).
On some topological problems of
operator theory, Ph.D. Thesis, Voronezh, 1972, 150 pp. (in Russian).
On Noetherian operators in a pair
of Banach spaces, Trudy Inst. Mat., Voronezh State Univ. Publ.,
1971, p.61-77 (in Russian).
(with S. Krein) An approach to the
interpolation of linear operators, Trudy Inst. Mat., Voronezh State
Univ. Publ., v.3, 1971, p.54-60 (in Russian).
On the problem of calculation of
flows in networks, in ''Applications of methods of mathematics and
computer science to solving of scientific and management problems'',
v.4, Voronezh State Univ. Publ., 1969, p.20-23 (in Russian).
(see also peer-reviewed papers,
books
and lecture
notes for students)
(with with G. Belitskii et al)
Yuri Il'ich Lyubich. April 22, 1931 - June 17, 2023. http://yuilyubich.com/in-memoriam.html.
(with A. Golberg and D. Shoikhet) Preface, in Harmonic Analysis and Partial Differential Equations: In Honor of Vladimir Maz'ya, Birkhauser, 2023, pp ix - xii.
P. Kuchment, Exploring the Radon Transform and the Field of Medical Imaging, Frome the SIAM Bookshelf, SIAM News, 2021.
M. Braverman, A. Dikanski, L. Friedlander, M. Gromov, V. Ivrii, Yu. Kordyukov, P. Kuchment, V. Maz'ya, T. Sunada, A. Zvonkin, Mikhail Aleksandrovich Shubin (1944-2020), AMS Notices, January 2021, 81 - 93.
M. Braverman, V. Buchstaber, M. Gromov, V. Ivrii, Yu. Kordyukov, P. Kuchment, V. Maz'ya, S. Novikov, T. Sunada, L. Friedlander, A. Khovanskii, Mikhail Aleksandrovich Shubin (1944-2020), Uspehi Mat. Nauk, 75(2020), V. 6, 162-170 (in Russian).
(Mark Agranovsky, John Baras, Der-Chen Chang, Roger Gay, Bao Qin Li, Peter Kuchment, Domenico Napoletani, Irene Sabadini, Ahmed Sebbar, Daniele C. Struppa, Alain Yger), Remembering Carlos A. Berenstein (1944-2019), Notices of the AMS, 67 (2020), no. 8.
(With V. Lin), Selim Krein and Voronezh Winter Mathematical Schools, in Differential Equations, Mathematical Physics, and Applications. Selim Grigorievich Krein Centennial, Contemporary Mathematics, Volume 734, 2019, pp 29-34.
(With Ye. Semenov), Introduction, in Functional Analysis and Geometry. Selim Grigorievich Krein Centennial, Contemporary Mathematics, Volume 734, 2019, pp 1-15.
(With Ye. Semenov), Introduction, in Differential Equations, Mathematical Physics, and Applications. Selim Grigorievich Krein Centennial, Contemporary Mathematics, Volume 734, 2019, pp 1-15.
(With Yu. Egorov, A. I. Komech, E. Lakshtanov, R. Novikov, V. Mazya, S. Molchanov, and M. Freidlin), ????? ????????? ???????? (Boris Rufimovich Vainberg), in Russian, Uspekhi Mat. Nauk (Russian Math Surveys), to appear.
(With V. Buchstaber, S. Novikov, and E. Semenov), ?????? ?????? ???????????? ?????? (1917 1998) (In memory of Selim Grigorievich Krein (1917-1988)), in Russian, Uspekhi Mat. Nauk, v. 73 (1018), no. 1, 187-193. In English: To the memory of Selim Grigor evich Krein (1917 1998), Russian Math Surveys 73 (2018), no 1, 191-193.
Leon Ehrenpreis, recollections from the recent decades , in I. Sabadini and D. Struppa (Editors) The Mathematical Legacy of Leon Ehrenpreis, Springer 2012, pp. 15 - 21.
(with L. Borcea, M. de Hoop, and G. Uhlmann) Inverse Problems and Applications, Emissary, Fall 2010, MSRI, Berkeley, CA.
(with H. Farkas, T. Kawai, T. E. Quinto, S. Sternberg, D. Struppa, and B. A. Taylor) Remembering Leon Ehrenpreis: 1930-2010, Notices of the Amer. Math. Soc. 58 (2011), no. 5, 674-681.
My dear teacher, in Memoirs on S. G. Krein, p. 36--41 Voronezh, Russia, 2002.
(with Yu. Berezansky, S. Gindikin, S. Kutateladze, S. Novikov, Yu. Reshetnyak, E. Semenov, S. Sklyadnev, and V. Tikhomirov) Selim Grigorievich Krein, Uspekhi Mat. Nauk 55(2000), no.2, 125-126.
(with S. Krein, V. Ovchinnikov, and E. Semenov) Iosif Shneiberg, in Israel Mathematical Conference Proceedings, vol. 13, AMS, Providence, RI 1999, 1-10.
Professor Selim Krein, in "Voronezh Winter Mathematical Schools. Dedicated to Professor Selim Krein", American Math. Society, providence, RI, 1998
(with E. Bolshakova) On the Fredholm property of an operator related to an abstract evolution equation with periodic coefficient, Theses of XIV school on operator theory, part 1, Novgorod, p. 26, 1989. (in Russian).
(with E. Bolshakova) On the Fredholm property of an operator generated by an abstract evolution equation with periodic operator coefficient, preprint, VINITI, no.1795-B89, 13 pp., 1989. (in Russian).
(with Ju. Berezanski, N. Bogolyubov, V. Maslov, S. Novikov and others) Selim Grigorievich Krein (to the 70-th birthday), Uspehi Mat Nauk, v. 42, no. 5, 1987, p. 223-224 (English translation in Russian Math. Surveys).
To the Floquet theory for an abstract evolution equation in a Hilbert space, preprint, VINITI, no. 3994-B86, 26 pp., 1986 (in Russian).
(with L. Khinkis) On spectral synthesis on semi-simple Lie groups, Proceedings of All-Union school on operator theory, Chelyabinsk, p. 72, 1986 (in Russian).
(with S. Krein and others) On the reconstruction of functions from empirical data with regard of an a priori information, preprint, VINITI, no. 1587-84, 53 pp., 1984 (in Russian).
An interpolation problem in the spaces of periodic entire functions of a finite order, preprint, VINITI, no. 4501-80, 1980 11 pp. (in Russian).
(with S. Lvin) On the absence of nonzero solutions in $L_2({\bf R}^n)$ for periodic PDEs, preprint, VINITI, no.2738-79, 1979, 11 pp. (in Russian).
(with L. Mogilevskaya) Positivity and analyticity of solutions of differential equations, Proceedings of All-Union Conf. on Diff. Equat., Moscow, 1976, p. 355-356 (in Russian).
On the problem of lifting of holomorphic functions with values in a factor-space of a Banach space, Proceedings of the Voronezh Winter Math. School, Voronezh State Univ. Publ., 1974, p.58 (in Russian).
(with L. Mogilevskaya) Some remarks about linear differential equations in a Banach space with a cone, Proceedings of the Voronezh Winter Math. School, Voronezh State Univ. Publ., 1974, p.74-75 (in Russian).
(with A. Pankov) Classifying spaces for the equivariant K-theory, Proceedings of the VIth All-Union Topological Conf., Tbilisi, 1972, p. 76 (in Russian).
Banach bundles and some topological questions of operator theory, Proceedings of the VIth All-Union Topological Conf., Tbilisi, 1972, p.75-76 (in Russian).
On dividing of a set into subsets of ''relatives'', in ``Collection of papers in math of students of Voronezh State Univ.'', 1967, p.167-169 (in Russian).
(with O. Shatalov and Z. Sunik) Lectures and problems, Texas A&M University SMaRT camp, 2019, 88pp. (Previous editions 2009 - 2013, 2016, 2017, 2018)
(with O. Shatalov and L. Kunyansky) Harmonic analysis and medical imaging, Texas A&M University SMaRT camp, 2018, 130pp.
(with G. Uhlmann) The Radon and X-Ray Transforms, 2010, 68pp.
Eclectic Notes on Distribution Theory, Fourier Transform, and Microlocal Analysis, 2009, 122pp.
.Geometry #4, Booklet for the Kansas Outreach School in Mathematics, WSU, Wichita, 1998
Geometry #3, Booklet for the Kansas Outreach School in Mathematics, WSU, Wichita, 1997
(with M. Alagic, Z. Jin, and K. Lancaster) Geometry #1, Booklet for the Kansas Outreach School in Mathematics, WSU, Wichita, 1996
(with M. Alagic, Z. Jin, and K. Lancaster) Geometry #2, Booklet for the Kansas Outreach School in Mathematics, WSU, Wichita, 1996
(with L. Mogilevskaya) Coordinates, Booklet for the Kansas Outreach School in Mathematics, WSU, Wichita, 1995, 30 pp.
(with L. Mogilevskaya and K. Swartzendruber) Functions and graphs #1. Linear, quadratic, and power functions, Booklet for the Kansas Outreach School in Mathematics, WSU, Wichita, 1995
(with L. Mogilevskaya and K. Starke) Inequalities #1, Booklet for the Kansas Outreach School in Mathematics, WSU, Wichita, 1995
(with K. Lancaster, L. Mogilevskaya, and P. Parker) Elements of Algebra, #1, Booklet for the Kansas Outreach School in Mathematics, WSU, Wichita, 1994, 79 pp.
(with L. Mogilevskaya) Elements of Algebra, #2, Booklet for the Kansas Outreach School in Mathematics, WSU, Wichita, 1994, 59 pp.
(with S. Lvin and others) BASIC programming and programs for lessons in mathematics, Voronezh Forestry Institute, parts 1-2,1987-1989, 52 pp. (in Russian).
Boolean algebras, switch circuits, and elements of reliability theory, Voronezh Forestry Institute, 26 pp. (in Russian), 1988.
Elements of network planning, chapter in S.Krein's book ''Mathematical programming'', Voronezh State Univ Publ. 1983.
Elements of network planning, Voronezh Forestry Institute, 22 pp. (in Russian)., 1976 .