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On Spectral Theory of Elliptic Operators

  • Book
  • © 1996

Overview

Authors:
  1. Yuri Egorov

    1. UPS, UFR MIG, Toulouse, France

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  2. Vladimir Kondratiev

    1. Faculty of Mathematics and Mechanics, Moscow State University, Moscow, Russia

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-X
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  2. Hilbert Spaces

    • Yuri Egorov, Vladimir Kondratiev
    Pages 1-24

  3. Functional Spaces

    • Yuri Egorov, Vladimir Kondratiev
    Pages 25-107

  4. Elliptic Operators

    • Yuri Egorov, Vladimir Kondratiev
    Pages 109-131

  5. Spectral Properties of Elliptic Operators

    • Yuri Egorov, Vladimir Kondratiev
    Pages 133-151

  6. The Sturm-Liouville Problem

    • Yuri Egorov, Vladimir Kondratiev
    Pages 153-206

  7. Differential Operators of Any Order

    • Yuri Egorov, Vladimir Kondratiev
    Pages 207-232

  8. Eigenfunctions of Elliptic Operators in Bounded Domains

    • Yuri Egorov, Vladimir Kondratiev
    Pages 233-273

  9. Negative Spectra of Elliptic Operators

    • Yuri Egorov, Vladimir Kondratiev
    Pages 275-317

  10. Back Matter

    Pages 319-332
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Keywords

About this book

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.

Authors and Affiliations

  • UPS, UFR MIG, Toulouse, France

    Yuri Egorov

  • Faculty of Mathematics and Mechanics, Moscow State University, Moscow, Russia

    Vladimir Kondratiev

Bibliographic Information

  • Book Title: On Spectral Theory of Elliptic Operators

  • Authors: Yuri Egorov, Vladimir Kondratiev

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-9029-8

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag 1996

  • Hardcover ISBN: 978-3-7643-5390-2Published: 30 July 1996

  • Softcover ISBN: 978-3-0348-9875-1Published: 27 September 2011

  • eBook ISBN: 978-3-0348-9029-8Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: X, 334

  • Topics: Analysis

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