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Orthogonal wavelets on the Cantor dyadic group. (English) Zbl 0841.42014

Summary: Based upon the shift operator as a dilation operator, multiresolution analyses are built on the Cantor dyadic group. A regularity condition is given for wavelets and sufficient conditions are given on scaling filters for regular orthonormal wavelets to occur. Examples of wavelets given include the Haar functions and certain lacunary Walsh function series analogous to the compactly supported wavelets of I. Daubechies.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
43A70 Analysis on specific locally compact and other abelian groups
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