Some topics on wavelet analysis (Q1309144)

This is a survey paper in which recent results in the following areas of wavelet analysis of functions in \(L^ p(\mathbb{R}^ d)\) are discussed: (1) the stability condition in the definition of a multiresolution analysis; (2) construction of wavelet bases (for \(p= 2\)); (3) use of the projection and quasi-interpolant to characterize Besov spaces and Triebel-Lizorkin spaces; (4) application of the Fourier method and the time domain method in the study of the ``refinement equation'' \(\varphi(n)= \sum a(n) \varphi(\alpha x- n)\), where \(a(0) a(N)\neq 0\) and \(\alpha> 1\), the sum is from \(n= 0\) to \(n= N\), and \(\varphi\) is a scaling function. There is a bibliography of 56 items, many from Chinese journals.