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On Riesz wavelets associated with multiresolution analyses. (English) Zbl 1017.42025

The authors obtain some properties that Riesz wavelets and the corresponding scaling functions should satisfy in order that the Riesz wavelets be associated with multiresolution analyses (MRA’s). They are given in terms of low/high pass filters and in terms of the Fourier transform by using a necessary and sufficient condition for the sum of two principal shift invariant spaces to be closed. These properties are used to obtain new characterizations of Riesz wavelets associated with MRA’s.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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