Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization
The book collects and contributes new results on the theory and practice of ill-posed inverse problems. Different notions of ill-posedness in Banach spaces for linear and nonlinear inverse problems are discussed not only in standard setting
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Jens Flemming
Source Conditions,
Variational
Quadratic
Inverse Problems, Sparsity Promoting
Regularization
Frontiers in Mathematics
Advisory Editorial Board Leonid Bunimovich (Georgia Institute of Technology, Atlanta) William Y. C. Chen (Nankai University, Tianjin, China) Benoît Perthame (Université Pierre et Marie Curie, Paris) Laurent Saloff-Coste (Cornell University, Ithaca) Igor Shparlinski (Macquarie University, New South Wales) Wolfgang Sprößig (TU Bergakademie Freiberg) Cédric Villani (Institut Henri Poincaré, Paris)
More information about this series at http://www.springer.com/series/5388
Jens Flemming
Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization New Results in Modern Theory of Inverse Problems and an Application in Laser Optics
Jens Flemming Fakult¨at f¨ur Mathematik Technische Universit¨at Chemnitz Chemnitz, Germany
ISSN 1660-8046 ISSN 1660-8054 (electronic) Frontiers in Mathematics ISBN 978-3-319-95263-5 ISBN 978-3-319-95264-2 (eBook) https://doi.org/10.1007/978-3-319-95264-2 Library of Congress Control Number: 2018950663 Mathematics Subject Classification (2010): 65J22, 65J20, 47A52, 47J06 © Springer Nature Switzerland AG 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Nature Switzerland AG part of Springer Nature. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
This book is dedicated to Bernd Hofmann on the occasion of his retirement.
Preface
This book grew out of the author’s habilitation thesis, which has been completed in January 2018. Parts II and III cover and slightly extend the material of the thesis. Part I, on the one hand, provides an introduction to the other parts and, on the other hand, contains new results on variation
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