توزیع حدی مقادیر ویژه اپراتورهای دیفرانسیل جزئی (ترجمه‌های مونوگراف‌های ریاضی)

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 self-contained and would be suitable as a graduate text. Ch. 1. Main Results -- Ch. 2. Oscillatory Integrals -- Ch. 3. Construction Of The Wave Group -- Ch. 4. Singularities Of The Wave Group -- Ch. 5. Proof Of Main Results -- Ch. 6. Mechanical Applications -- Appendix A. Spectral Problem On The Half-line / A. Holst -- Appendix B. Fourier Tauberian Theorems / M. Levitin -- Appendix C. Stationary Phase Formula -- Appendix D. Hamiltonian Billiards: Proofs -- Appendix E. Factorization Of Smooth Functions And Taylor-type Formulae. Yu. Safarov, D. Vassiliev. Translated By The Authors From An Unpublished Russian Manuscript. Includes Bibliographical References (p. - ) And Indexes. Studies the eigenvalues of elliptic linear boundary value problems. This work features a collection of asymptotic formulas describing the distribution of eigenvalues with high sequential numbers. It provides an introduction to the mathematical concepts and tools, such as microlocal analysis, billiards, symplectic geometry and Tauberian theorems. This work studies the eigenvalues of elliptic linear boundary value problems. Its main content is a set of asymptotic formulas describing the distribution of eigenvalues with high sequential numbers, providing a basic introduction to mathematical concepts and tools