Introductory statement

VIGRE seminar course announcement: Asymptotic and Numerical Approaches to Spectral and PDE Problems

Minakshisundaram and the birth of geometric spectral asymptotics, Indian Journal for the Advancement of Mathematics Education and Research 32 (2004) 95-99

Recent papers on spectral theory and asymptotics

• Short exposition: S. A. Fulling, What we should have learned from G. H. Hardy about quantum field theory under external conditions, in The Casimir Effect 50 Years Later, ed. by M. Bordag (World Scientific, Singapore, 1999), pp. 145-154. Preprint available (DVI) (PS) (PDF)
• S. A. Fulling (with appendix by R. A. Gustafson), Some properties of Riesz means and spectral expansions, Electron. J. Diff. Eqs. 1999 No. 6, 1-39 (1999)
• R. Estrada and S. A. Fulling, Distributional asymptotic expansions of spectral functions and of the associated Green kernels, Electron. J. Diff. Eqs. 1999 No. 7, 1-37 (1999)
• Numerical examples by Christopher Romero
• S. A. Fulling, E. V. Gorbar, and C. T. Romero, Spectral Riesz-Cesaro means: How the square root function helps us to see around the world, Electron. J. Diff. Eqs., Conf. 04, 2000, pp. 87-101.
• J. D. Bondurant and S. A. Fulling, The Dirichlet-to-Robin transform. J. Phys. A 38 (2005) 1505-1532
• S. A. Fulling and P. Kuchment, Coincidence of length spectra does not imply isospectrality, Inverse Problems 21 (2005) 1391-1395
• Y. Yang and S. A. Fulling, Some Subtleties in the Relationships among Heat Kernel Invariants, Eigenvalue Distributions, and Quantum Vacuum Energy, J. Phys. A 48 (2015) 045402

• Ross McDonald's Undergraduate Research Scholar thesis on Neumann partitions

See also Semiclassical approximations and Vacuum energy.

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