The Joint Spectral Radius: Theory and Applications

ISBN-13: 9783540959793 / Angielski / Miękka / 2009 / 146 str.

Raphael Jungers

Opis

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.

Recenzje

From the reviews:

"This very interesting and well-written monograph covers both the theory and several applications of the joint spectral radius of a set of matrices, a notion which appears in different fields of mathematics ... . The monograph is made of two parts: the first addresses the theoretical aspects, while the second is focused on some applications. ... I believe the book will become a standard reference for the subject." (Nicola Guglielmi, Mathematical Reviews, Issue 2011 c)

Spis treści

I Theory.- Basics.- Classical Results and Problems.- Nonnegative Integer Matrices.- On the Finiteness Property for Rational Matrices.- II Applications.- Continuity of Wavelet Functions.- Capacity of Codes.- Overlap-Free Words.- Trackable Graphs.- Conclusion.- III Appendices.- Appendix A Numerical Values for Overlap-Free Words.