Softcover ISBN:  9780821809211 
Product Code:  MMONO/155.S 
354 pp 
List Price:  $122.00 
MAA Member Price:  $109.80 
AMS Member Price:  $97.60 
Electronic ISBN:  9781470445706 
Product Code:  MMONO/155.E 
354 pp 
List Price:  $122.00 
MAA Member Price:  $109.80 
AMS Member Price:  $97.60 

Book DetailsTranslations of Mathematical MonographsVolume: 155; 1997MSC: Primary 35; 58;
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.ReadershipGraduate students, research mathematicians, applied mathematicians, engineers, and physicists interested in partial differential equations.

Table of Contents

Chapters

Chapter 1. Main results

Chapter 2. Oscillatory integrals

Chapter 3. Construction of the wave group

Chapter 4. Singularities of the wave group

Chapter 5. Proof of main results

Chapter 6. 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


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


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

Chapters

Chapter 1. Main results

Chapter 2. Oscillatory integrals

Chapter 3. Construction of the wave group

Chapter 4. Singularities of the wave group

Chapter 5. Proof of main results

Chapter 6. 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

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