Stable Approximate Evaluation of Unbounded Operators
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 provi
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Groetsch
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LNM 1894
ISSN 0075-8434 ISBN 3-540-39942-1
BarCode
9 7 8 3 5 4 0 3 99 4 2 1
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Charles W. Groetsch
Stable Approximate Evaluation of Unbounded Operators
1894
Stable Approximate Evaluation of Unbounded Operators
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 TikhonovMorozov method and its iterated version.
Lecture Notes in Mathematics
Lecture Notes in Mathematics
1 23
Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
1894
Charles W. Groetsch
Author Charles W. Groetsch The Traubert Chair School of Science and Mathematics The Citadel Charleston, SC 29409 USA e-mail: [email protected]
Library of Congress Control Number: 2006931917 Mathematics Subject Classification (2000): Primary: 47A52, 65J20; Secondary: 47A58, 65J22 ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 ISBN-10 3-540-39942-9 Springer Berlin Heidelberg New York ISBN-13 978-3-540-39942-1 Springer Berlin Heidelberg New York DOI 10.1007/3-540-39942-9 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the
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