## Smoothness of Wavelet and Joint Spectral Radius

J. Math. Sci. Univ. Tokyo
Vol. 5 (1998), No. 2, Page 241--256.

En, Tei
Smoothness of Wavelet and Joint Spectral Radius
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

Abstract:
For a dilation equation $f(x)=\sum_{k=0}^Nc_k\,f(2x-k)$ where coefficients $\{c_j\}$ satisfy suitable conditions, we can define a function $Î±_{\max}(c_0, \ldots, c_N):=\sup\{Î±$; $f$ is HÃ¶lder continuous with exponent $Î±\}$ as a function of $\{c_j\}$ on a set $C_X$ which is a subset of an $(N-1)$-dimensional space $X$. We prove that the set of discontinuous points of $Î±_{\max}$ is of measure zero in $X$. We also prove some new formulas concerning the joint spectral radius.

Keywords: wavelets, joint spectral radius

Mathematics Subject Classification (1991): Primary 42C15; Secondary 39A10
Mathematical Reviews Number: MR1633925