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Linear Integral Equations

  • Book
  • © 1999

Overview

Authors:
  1. Rainer Kress

    1. Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Göttingen, Germany

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Part of the book series: Applied Mathematical Sciences (AMS, volume 82)

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Normed Spaces

    • Rainer Kress
    Pages 1-14

  3. Bounded and Compact Operators

    • Rainer Kress
    Pages 15-27

  4. Riesz Theory

    • Rainer Kress
    Pages 28-38

  5. Dual Systems and Fredholm Alternative

    • Rainer Kress
    Pages 39-54

  6. Regularization in Dual Systems

    • Rainer Kress
    Pages 55-66

  7. Potential Theory

    • Rainer Kress
    Pages 67-93

  8. Singular Integral Equations

    • Rainer Kress
    Pages 94-124

  9. Sobolev Spaces

    • Rainer Kress
    Pages 125-151

  10. The Heat Equation

    • Rainer Kress
    Pages 152-162

  11. Operator Approximations

    • Rainer Kress
    Pages 163-176

  12. Degenerate Kernel Approximation

    • Rainer Kress
    Pages 177-196

  13. Quadrature Methods

    • Rainer Kress
    Pages 197-217

  14. Projection Methods

    • Rainer Kress
    Pages 218-246

  15. Iterative Solution and Stability

    • Rainer Kress
    Pages 247-264

  16. Equations of the First Kind

    • Rainer Kress
    Pages 265-289

  17. Tikhonov Regularization

    • Rainer Kress
    Pages 290-307

  18. Regularization by Discretization

    • Rainer Kress
    Pages 308-319

  19. Inverse Boundary Value Problems

    • Rainer Kress
    Pages 320-346

  20. Back Matter

    Pages 347-367
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Keywords

About this book

In the ten years since the first edition of this book appeared, integral equations and integral operators have revealed more of their mathematical beauty and power to me. Therefore, I am pleased to have the opportunity to share some of these new insights with the readers of this book. As in the first edition, the main motivation is to present the fundamental theory of integral equations, some of their main applications, and the basic concepts of their numerical solution in a single volume. This is done from my own perspective of integral equations; I have made no attempt to include all of the recent developments. In addition to making corrections and adjustments throughout the text and updating the references, the following topics have been added: In Sec­ tion 4.3 the presentation of the Fredholm alternative in dual systems has been slightly simplified and in Section 5.3 the short presentation on the index of operators has been extended. The treatment of boundary value problems in potential theory now includes proofs of the jump relations for single-and double-layer potentials in Section 6.3 and the solution of the Dirichlet problem for the exterior of an arc in two dimensions (Section 7.6). The numerical analysis of the boundary integral equations in Sobolev space settings has been extended for both integral equations of the first kind in Section 13.4 and integral equations of the second kind in Section 12.4.

Authors and Affiliations

  • Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Göttingen, Germany

    Rainer Kress

Bibliographic Information

  • Book Title: Linear Integral Equations

  • Authors: Rainer Kress

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-1-4612-0559-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1999

  • eBook ISBN: 978-1-4612-0559-3Published: 06 December 2012

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 2

  • Number of Pages: XIV, 367

  • Topics: Analysis

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