Lecture Notes in Mathematics
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Stable Approximate Evaluation of Unbounded Operators

Authors: Groetsch, Charles W.

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About this book

Spectral theory of bounded linear operators teams up with von Neumann’s theory of unbounded operators in this monograph to provide a general framework for the study of stable methods for the evaluation of unbounded operators. An introductory chapter provides numerous illustrations of unbounded linear operators that arise in various inverse problems of mathematical physics. Before the general theory of stabilization methods is developed, an extensive exposition of the necessary background material from the theory of operators on Hilbert space is provided. Several specific stabilization methods are studied in detail, with particular attention to the Tikhonov-Morozov method and its iterated version.

Reviews

From the reviews:

"This interesting monograph is devoted to the stable evaluation of the action of unbounded operators defined on Hilbert spaces. This problem is considered as an abstract mathematical problem within the scope of operator approximation theory. To motivate the discussion, the mathematical theory of inverse problems is briefly introduced. … The monograph is reasonably self-contained and elegantly written. It gradually invites the reader to learn more about the difficulties of solving ill-posed problems." (Antonio C. G. Leitão, Mathematical Reviews, Issue 2008 a)

“The author does an excellent job of covering the subject of the title in 120 pages and five chapters … . the monograph would make a nice graduate course or seminar in applied mathematics.” (John R. Cannon, SIAM Review, Vol. 52 (2), 2010)


Table of contents (5 chapters)

Table of contents (5 chapters)
  • Some Problems Leading to Unbounded Operators

    Pages 1-17

  • Hilbert Space Background

    Pages 19-51

  • A General Approach to Stabilization

    Pages 53-75

  • The Tikhonov-Morozov Method

    Pages 77-99

  • Finite-Dimensional Approximations

    Pages 101-119

Buy this book

eBook $34.99
price for USA in USD
  • ISBN 978-3-540-39943-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA in USD
  • ISBN 978-3-540-39942-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Stable Approximate Evaluation of Unbounded Operators
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1894
Copyright
2007
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-39943-8
DOI
10.1007/3-540-39942-9
Softcover ISBN
978-3-540-39942-1
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 133
Topics