**Translations of Mathematical Monographs**

1997;
354 pp;
Softcover

MSC: Primary 35; 58;

**Print ISBN: 978-0-8218-0921-1
Product Code: MMONO/155.S**

List Price: $122.00

AMS Member Price: $97.60

MAA Member Price: $109.80

**Electronic ISBN: 978-1-4704-4570-6
Product Code: MMONO/155.E**

List Price: $122.00

AMS Member Price: $97.60

MAA Member Price: $109.80

# The Asymptotic Distribution of Eigenvalues of Partial Differential Operators

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*Yu. Safarov; D. Vassiliev*

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.

#### Readership

Graduate students, research mathematicians, applied mathematicians, engineers, and physicists interested in partial differential equations.

#### Reviews & Endorsements

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

# Table of Contents

## The Asymptotic Distribution of Eigenvalues of Partial Differential Operators

- Cover Cover11
- Title page v6
- Contents vii8
- Preface xi12
- Chapter 1. Main results 116
- Chapter 2. Oscillatory integrals 6378
- Chapter 3. Construction of the wave group 129144
- Chapter 4. Singularities of the wave group 167182
- Chapter 5. Proof of main results 193208
- Chapter 6. Mechanical applications 229244
- Appendix A. Spectral problem on the half-line 251266
- Appendix B. Fourier Tauberian theorems 297312
- Appendix C. Stationary phase formula 307322
- Appendix D. Hamiltonian billiards: Proofs 313328
- Appendix E. Factorization of smooth functions and Taylor-type formulae 335350
- References 343358
- Principal notation 349364
- Index 353368
- Back Cover Back Cover1370