The Joint Spectral Radius Theory and Applications
This monograph is based on the Ph.D. Thesis of the author [58]. Its goal is twofold: First, it presents most researchwork that has been done during his Ph.D., or at least the part of the work that is related with the joint spectral radius. This work was c
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Raphaël Jungers
The Joint Spectral Radius Theory and Applications
ABC
Series Advisory Board P. Fleming, P. Kokotovic, A.B. Kurzhanski, H. Kwakernaak, A. Rantzer, J.N. Tsitsiklis
Author Raphaël Jungers UCL/INMA Avenue Georges Lemaître, 4-6 1348 Louvain-la-Neuve Belgium E-mail: [email protected]
ISBN 978-3-540-95979-3
e-ISBN 978-3-540-95980-9
DOI 10.1007/978-3-540-95980-9 Lecture Notes in Control and Information Sciences
ISSN 0170-8643
Library of Congress Control Number: Applied for c 2009
Springer-Verlag Berlin Heidelberg
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, 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. Typeset & Cover Design: Scientific Publishing Services Pvt. Ltd., Chennai, India. Printed in acid-free paper 543210 springer.com
To my parents Non scholae sed vitae discimus
Preface
This monograph is based on the Ph.D. Thesis of the author [58]. Its goal is twofold: First, it presents most research work that has been done during his Ph.D., or at least the part of the work that is related with the joint spectral radius. This work was concerned with theoretical developments (part I) as well as the study of some applications (part II). As a second goal, it was the author’s feeling that a survey on the state of the art on the joint spectral radius was really missing in the literature, so that the first two chapters of part I present such a survey. The other chapters mainly report personal research, except Chapter 5 which presents an important application of the joint spectral radius: the continuity of wavelet functions. The first part of this monograph is dedicated to theoretical results. The first two chapters present the above mentioned survey on the joint spectral radius. Its minimum-growth counterpart, the joint spectral subradius, is also considered. The next two chapters point out two specific theoretical topics, that are important in practical applications: the particular case of nonnegative matrices, and the Finiteness Property. The second part considers applications involving the joint spectral radius. We first present the continuity of wavelets. We then study the problem of the capacity of codes submitted to forbidden difference constraints. Then we go to the notion of overlap-free words, a problem that arises in combinatorics on wo
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