Tensor Valuations and Their Applications in Stochastic Geometry and Imaging
The purpose of this volume is to give an up-to-date introduction to tensor valuations and their applications. Starting with classical results concerning scalar-valued valuations on the families of convex bodies and convex polytopes, it proceeds to the mod
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Eva B. Vedel Jensen Markus Kiderlen Editors
Tensor Valuations and Their Applications in Stochastic Geometry and Imaging
Lecture Notes in Mathematics Editors-in-Chief: Jean-Michel Morel, Cachan Bernard Teissier, Paris Advisory Board: Michel Brion, Grenoble Camillo De Lellis, Zurich Mario Di Bernardo, Bristol Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gábor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, New York Anna Wienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
Eva B. Vedel Jensen • Markus Kiderlen Editors
Tensor Valuations and Their Applications in Stochastic Geometry and Imaging
123
Editors Eva B. Vedel Jensen Department of Mathematics Aarhus University Aarhus C, Denmark
ISSN 0075-8434 Lecture Notes in Mathematics ISBN 978-3-319-51950-0 DOI 10.1007/978-3-319-51951-7
Markus Kiderlen Department of Mathematics Aarhus University Aarhus C, Denmark
ISSN 1617-9692 (electronic) ISBN 978-3-319-51951-7 (eBook)
Library of Congress Control Number: 2017942766 © Springer International Publishing AG 2017 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. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
The purpose of this volume is to give an up-to-date introduction to tensor valuations and their applications on a graduate level. A valuation is a finitely additive mapping. Since Dehn’s use of real-valued valuations to give a negative answer to Hilbert’s third problem in 1900, the theory of valuations has been extended considerably and found widespread use in applied sciences like biology, materials sciences, medicine and physics. At the end of the twentieth century, McMullen an
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