Lapidus M., et al. - Fractal Geometry, Complex Dimensions and Zeta Functions (Springer, 2006).pdf

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S pringer M onographs in M athematics
To my Riemann zeros :
Odile, Julie and Michael, my muse and offspring
Michel L. Lapidus
To Jena, David and Samuel
Machiel van Frankenhuijsen
Michel L. Lapidus Machiel van Frankenhuijsen
Fractal Geometry,
Complex Dimensions
and Zeta Functions
Geometry and Spectra of Fractal Strings
With 53 Illustrations
100515366.002.png 100515366.003.png
Michel L. Lapidus
University of California
Department of Mathematics
231 Surge Building
Riverside, CA 92521-0135
USA
lapidus@math.ucr.edu
Machiel van Frankenhuijsen
Utah Valley State College
Department of Mathematics
800 West University Parkway
Orem, Utah 84058-5999
USA
vanframa@uvsc.edu
The front cover shows a tubular neighborhood of the Devil’s staircase (Figure 12.2, page 335)
and the quasiperiodic pattern of the complex dimensions of a nonlattice self-similar string
(Figure 3.7, page 86).
Mathematics Subject Classification (2000): Primary–11M26, 11M41, 28A75, 28A80, 35P20, 58G25
Secondary–11J70, 11M06, 11N05, 28A12, 30D35, 81Q20
Library of Congress Control Number: 2006929212
ISBN-10: 0-387-33285-5
e-ISBN: 0-387-35208-2
ISBN-13: 978-0-387-33285-7
Printed on acid-free paper.
©2006 Springer Science+Business Media, LLC
All rights reserved. This work may not be translated or copied in whole or in part without the written
permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York,
NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in
connection with any form of information storage and retrieval, electronic adaptation, computer
software, or by similar or dissimilar methodology now known or hereafter developed is forbidden.
The use in this publication of trade names, trademarks, service marks, and similar terms, even if they
are not identified as such, is not to be taken as an expression of opinion as to whether or not they are
subject to proprietary rights.
Printed in the United States of America.
(EB)
987654321
springer.com

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