Translations of Mathematical Monographs 1997; 354 pp; softcover Volume: 155 Reprint/Revision History: reprinted with corrections 1998 ISBN10: 0821809210 ISBN13: 9780821809211 List Price: US$122 Member Price: US$97.60 Order Code: MMONO/155.S
 As the subject of extensive research for over a century, spectral asymptotics for partial differential operators attracted the attention of many outstanding mathematicians and physicists. This book studies the eigenvalues of elliptic linear boundary value problems and has as its main content a collection of asymptotic formulas describing the distribution of eigenvalues with high sequential numbers. Asymptotic formulas are used to illustrate standard eigenvalue problems of mechanics and mathematical physics. The volume provides a basic introduction to all the necessary mathematical concepts and tools, such as microlocal analysis, billiards, symplectic geometry and Tauberian theorems. It is selfcontained and would be suitable as a graduate text. Readership Graduate students, research mathematicians, applied mathematicians, engineers, and physicists interested in partial differential equations. Reviews "In the reviewer's opinion, this book is indispensable for serious students of spectral asymptotics."  Lars Hörmander for the Bulletin of the London Mathematical Society Table of Contents  Main results
 Oscillatory integrals
 Construction of the wave group
 Singularities of the wave group
 Proof of main results
 Mechanical applications
 Appendix A. Spectral problem on the halfline
 Appendix B. Fourier Tauberian theorems
 Appendix C. Stationary phase formula
 Appendix D. Hamiltonian billiards: proofs
 Appendix E. Factorization of smooth functions and Taylortype formulae
 References
 Principal notation
 Index
