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On Spectral Theory of Elliptic Operators

  • Yuri Egorov
  • Vladimir Kondratiev

Part of the Operator Theory Advances and Applications book series (OT, volume 89)

Table of contents

  1. Front Matter
    Pages I-X
  2. Yuri Egorov, Vladimir Kondratiev
    Pages 1-24
  3. Yuri Egorov, Vladimir Kondratiev
    Pages 25-107
  4. Yuri Egorov, Vladimir Kondratiev
    Pages 109-131
  5. Yuri Egorov, Vladimir Kondratiev
    Pages 133-151
  6. Yuri Egorov, Vladimir Kondratiev
    Pages 153-206
  7. Yuri Egorov, Vladimir Kondratiev
    Pages 207-232
  8. Yuri Egorov, Vladimir Kondratiev
    Pages 233-273
  9. Yuri Egorov, Vladimir Kondratiev
    Pages 275-317
  10. Back Matter
    Pages 319-332

About this book

Introduction

It is well known that a wealth of problems of different nature, applied as well as purely theoretic, can be reduced to the study of elliptic equations and their eigen-values. During the years many books and articles have been published on this topic, considering spectral properties of elliptic differential operators from different points of view. This is one more book on these properties. This book is devoted to the study of some classical problems of the spectral theory of elliptic differential equations. The reader will find hardly any intersections with the books of Shubin [Sh] or Rempel-Schulze [ReSch] or with the works cited there. This book also has no general information in common with the books by Egorov and Shubin [EgShu], which also deal with spectral properties of elliptic operators. There is nothing here on oblique derivative problems; the reader will meet no pseudodifferential operators. The main subject of the book is the estimates of eigenvalues, especially of the first one, and of eigenfunctions of elliptic operators. The considered problems have in common the approach consisting of the application of the variational principle and some a priori estimates, usually in Sobolev spaces. In many cases, impor­ tant for physics and mechanics, as well as for geometry and analysis, this rather elementary approach allows one to obtain sharp results.

Keywords

Fourier transform Hilbert space Self-adjoint operator Variable equation function partial differential equations spectral theory theorem

Authors and affiliations

  • Yuri Egorov
    • 1
  • Vladimir Kondratiev
    • 2
  1. 1.UPS, UFR MIGToulouseFrance
  2. 2.Faculty of Mathematics and MechanicsMoscow State UniversityMoscowRussia

Bibliographic information

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