Discourses in Mathematics and Its Applications, No. 1 1991

Forty More Years of Ramifications: Spectral Asymptotics and Its Applications

Edited by S. A. Fulling and F. J. Narcowich

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Ramifications, Old and New, of the Eigenvalue Problem (reprinted from Bulletin of the American Mathematical Society, 1950) … 1

Hermann Weyl

The Uses and Implications of Curved-Spacetime Propagators: A Personal View (Dirac Medal Lecture) . . . . . . . . . . . . . . . . . . . . . . . . 27

Bryce S. DeWitt

Summation and Spectral Theory of Eigenfunction Expansions . . . . . . . 49 Mark Kon

The Inverse Spectral Problem . . . . . . . . . . . . . . . . . . . . . 77 David Gurarie

Wave Problems in Terms of Complex Classical Paths . . . . . . . . . . 101 Roger Balian

Phase-Integral Approximation of Arbitrary Order Generated from an Unspecified Base Function . . . . . . . . . . . . . . . . . . . . . 121

Nanny Fröman and Per Olof Fröman

Time-Reversal Invariance and the Time-Dependent Born–Oppenheimer Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . 161

George A. Hagedorn

The Wigner-Weyl Transform on Tori and Connected Graph Propagator Representations . . . . . . . . . . . . . . . . . . . . . . . . . . 199

Thomas A. Osborn and Frank H. Molzahn

Eigenvalue Problems Related to Finite Analogues of Upper Half Planes . . 237 Audrey Terras

The Index Theorem and Clifford Modules . . . . . . . . . . . . . . . 265 Peter B. Gilkey