Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction

  • Authors
  • Dang Dinh Ang
  • Rudolf Gorenflo
  • Vy Khoi Le
  • Dang Duc Trong

Part of the Lecture Notes in Mathematics book series (LNM, volume 1792)

Table of contents

  1. Front Matter
    Pages N2-viii
  2. Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong
    Pages 1-3
  3. Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong
    Pages 5-16
  4. Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong
    Pages 17-49
  5. Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong
    Pages 51-81
  6. Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong
    Pages 83-97
  7. Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong
    Pages 99-130
  8. Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong
    Pages 131-146
  9. Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong
    Pages 147-169
  10. Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong
    Pages 171-173
  11. Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong
    Pages 175-180
  12. Dang Dinh Ang, Rudolf Gorenflo, Vy Khoi Le, Dang Duc Trong
    Pages 181-183
  13. Back Matter
    Pages 185-185

About this book

Introduction

Moment Theory is not a new subject; however, in classical treatments, the ill-posedness of the problem is not taken into account - hence this monograph. Assuming a "true" solution to be uniquely determined by a sequence of moments (given as integrals) of which only finitely many are inaccurately given, the authors describe and analyze several regularization methods and derive stability estimates. Mathematically, the task often consists in the reconstruction of an analytic or harmonic function, as is natural from concrete applications discussed (e.g. inverse heat conduction problems, Cauchy's problem for the Laplace equation, gravimetry). The book can be used in a graduate or upper undergraduate course in Inverse Problems, or as supplementary reading for a course on Applied Partial Differential Equations.

Keywords

Moment problems Potential theory inverse problems partial differential equation reconstruction of analytic functions regularization methods

Bibliographic information

  • DOI https://doi.org/10.1007/b84019
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-44006-2
  • Online ISBN 978-3-540-45658-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book