Extensions of Positive Definite Functions Applications and Their Har
This monograph deals with the mathematics of extending given partial data-sets obtained from experiments; Experimentalists frequently gather spectral data when the observed data is limited, e.g., by the precision of instruments; or by other limiting
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Palle Jorgensen Steen Pedersen Feng Tian
Extensions of Positive Definite Functions Applications and Their Harmonic Analysis
Lecture Notes in Mathematics Editors-in-Chief: J.-M. Morel, Cachan B. Teissier, Paris Advisory Board: Camillo De Lellis, Zurich Mario di Bernardo, Bristol Alessio Figalli, Austin Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gabor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, Paris and New York Catharina Stroppel, Bonn Anna Wienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
Palle Jorgensen • Steen Pedersen • Feng Tian
Extensions of Positive Definite Functions Applications and Their Harmonic Analysis
123
Steen Pedersen Department of Mathematics Wright State University Dayton Ohio, USA
Palle Jorgensen Department of Mathematics The University of Iowa Iowa City Iowa, USA Feng Tian Mathematics Department Hampton University Hampton Virginia, USA
ISSN 0075-8434 Lecture Notes in Mathematics ISBN 978-3-319-39779-5 DOI 10.1007/978-3-319-39780-1
ISSN 1617-9692 (electronic) ISBN 978-3-319-39780-1 (eBook)
Library of Congress Control Number: 2016944420 © Springer International Publishing Switzerland 2016 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. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
Dedicated to the memory of William B. Arveson1 (November 22, 1934–November 15, 2011) Edward Nelson2 (May 4, 1932–September 10, 2014) 1 William Arveson (1934–2011) worked on operator algebras and harmonic analysis, and his results have been influential in our thinking and in our approach to the particular extension questions we consider here. In fact, Arveson’s deep and pioneering work on completely positive maps may be thought of as a noncommutative variant of our present extension questions. We have chosen to give our results in the commutative setting, but readers with inte
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