Pseudodifferential Equations Over Non-Archimedean Spaces
Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelf
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W. A. Zúñiga-Galindo
Pseudodifferential Equations Over Non-Archimedean Spaces
Lecture Notes in Mathematics Editors-in-Chief: J.-M. Morel, Cachan B. Teissier, Paris Advisory Board: Camillo De Lellis, Zurich Mario di Bernardo, Bristol Michel Brion, Grenoble Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gabor 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
W.A. ZúQniga-Galindo
Pseudodifferential Equations Over Non-Archimedean Spaces
123
W.A. ZúQniga-Galindo Department of Mathematics Center for Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV) Mexico City, Mexico
ISSN 0075-8434 Lecture Notes in Mathematics ISBN 978-3-319-46737-5 DOI 10.1007/978-3-319-46738-2
ISSN 1617-9692 (electronic) ISBN 978-3-319-46738-2 (eBook)
Library of Congress Control Number: 2016963106 Mathematics Subject Classification (2010): 11-XX; 43-XX; 46-XX; 60-XX; 70-XX © Springer International Publishing AG 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 The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Dedicated to my wife Mónica, my daughter Daniela, and my son Felipe
Preface
In recent years, p-adic analysis (or more generally non-Archimedean analysis) has received a lot of attention due to its connections with mathematical physics; see, e.g., [8–14, 20, 21, 25, 26, 36, 64, 65, 67–69, 75, 76, 80, 82, 85–87, 90, 94, 106–109, 111] and references therein. All these developments have been motivated by two physical ideas. The first is the conjecture (due to I. Volovich) in particle physics that at Planck distances the space-time has a non-Archimedean structure; see, e.g., [107, 112, 113]. The second idea comes from statistical physi
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