Fractal Zeta Functions and Fractal Drums Higher-Dimensional Theory o
This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums
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Michel L. Lapidus Goran Radunović Darko Žubrinić
Fractal Zeta Functions and Fractal Drums Higher-Dimensional Theory of Complex Dimensions
Springer Monographs in Mathematics
More information about this series at http://www.springer.com/series/3733
Michel L. Lapidus Goran Radunovi´c ˇ Darko Zubrini´ c
Fractal Zeta Functions and Fractal Drums Higher-Dimensional Theory of Complex Dimensions With 52 illustrations
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Michel L. Lapidus Department of Mathematics University of California Riverside, California, USA
Goran Radunovi´c Department of Applied Mathematics University of Zagreb Zagreb, Croatia
ˇ Darko Zubrini´ c Department of Applied Mathematics University of Zagreb Zagreb, Croatia
ISSN 1439-7382 ISSN 2196-9922 (electronic) Springer Monographs in Mathematics ISBN 978-3-319-44704-9 ISBN 978-3-319-44706-3 (eBook) DOI 10.1007/978-3-319-44706-3 Library of Congress Control Number: 2016954237 Mathematics Subject Classification (2010): Primary – 11M41, 28A12, 28A75, 28A80, 28B15, 30D10, 35P20, 42B20, 44A05, 58J32; Secondary – 11M06, 30D30, 37C30, 37C45, 40A10, 42B35, 42B37, 44A10, 45Q05, 81Q20 © Springer International Publishing Switzerland 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
To my wife, Odile, with infinite love To my beautiful and extraordinary children Julie Anne Myriam and Michael Alex Serge Michel L. Lapidus
To my parents Nevenka n´ee Bili´c and Ranko Goran Radunovi´c
To the memory of my parents Katarina n´ee Sunteˇsi´c and Velimir ˇ Darko Zubrini´ c
Overview
Recently, the first author has extended the definition of the zeta function associated with fractal strings to arbitrary bounded subsets A of the N-dime
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