Abstract
This chapter presents a brief survey of an important application of the joint spectral radius: the continuity of wavelet functions. Historically, this application seems to have motivated the interest of mathematicians for the joint spectral radius. This, and the fact that this application of the joint spectral radius is perhaps the one that has the greatest impact on the industry, motivates the existence of this small chapter. Our goal here is not to provide a survey of wavelet theory. We will limit ourself to present how the joint spectral radius allows to characterize the regularity of certain wavelets (Sections 5.1 and 5.2). In Section 5.3 we present two examples of such wavelets.
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© 2009 Springer-Verlag Berlin Heidelberg
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Jungers, R. (2009). Continuity of Wavelet Functions. In: The Joint Spectral Radius. Lecture Notes in Control and Information Sciences, vol 385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-95980-9_6
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DOI: https://doi.org/10.1007/978-3-540-95980-9_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-95979-3
Online ISBN: 978-3-540-95980-9
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