Abstract:
In the spaces of complex periodic sequences, we use the Vilenkin–Chrestenson transforms to construct new orthogonal wavelet bases defined by finite collections of parameters. Earlier similar bases were defined for the Cantor and Vilenkin groups by means of generalized Walsh functions. It is noted that similar constructions can be realized for biorthogonal wavelets as well as for the space $\ell^2(\mathbb{Z}_+)$.
Keywords:Walsh functions, Haar basis, Cantor group, Vilenkin–Chrestenson transform, Hausholder transform, discrete wavelets, biorthogonal wavelets, multiresolution analysis, complex periodic sequences.
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