The joint spectral radius: Theory and applications

Raphaël Jungers (auth.)3540959793, 9783540959793

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 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 ?rst two chapters of part I present such a survey. The other chapters mainly report personal research, except Chapter 5 which presents animportantapplicationofthejointspectralradius:thecontinuityofwavelet functions. The ?rst part of this monograph is dedicated to theoretical results. The ?rst 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 speci?c theoretical topics, that are important in practical applications: the particular case of nonne- tive matrices, and the Finiteness Property. The second part considers applications involving the joint spectral radius.

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Table of contents :
Front Matter….Pages –
Introduction….Pages 1-3
Front Matter….Pages 5-5
Basics….Pages 7-22
Classical Results and Problems….Pages 23-46
Nonnegative Integer Matrices….Pages 47-61
On the Finiteness Property for Rational Matrices….Pages 63-74
Front Matter….Pages 75-75
Continuity of Wavelet Functions….Pages 77-84
Capacity of Codes….Pages 85-99
Overlap-Free Words….Pages 101-114
Trackable Graphs….Pages 115-120
Conclusion….Pages 121-123
Front Matter….Pages 125-125
Appendix A Numerical Values for Overlap-Free Words….Pages 127-131
Back Matter….Pages –