Compactly supported orthogonal symmetric scaling functions
\textit{I. Daubechies} [Commun. Pure Appl. Math. 41, No. 7, 909-996 (1988; Zbl 0644.42026)] showed that, except for the Haar function, there exist no compactly supported orthogonal symmetric scaling functions for the dilation \(q=2\). However, such scaling functions do exist for \(q>2\), as shown by \textit{Ch. K. Chui} and \textit{J.-A. Lian} [Appl. Comput. Harmon. Anal. 2, No. 1, 21-51 (1995; Zbl 0814.42016)] for the case \(q=3\). These functions are the main object of the paper under review. The authors construct new symmetric scaling functions and introduce the ``Batman'' family of continuous symmetric scaling functions with very small supports. They establish the exact smoothness of the ``Batman'' scaling functions using the joint spectral radius technique.
scientific article; zbMATH DE number 1382914
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