Wavelets on Discrete Fields

Abstract : An arithmetic version of continuous wavelet analysis is described. Starting from a square-integrable representation of the affine group of Z Z p (or Z Z) it is shown how wavelet decom-positions of ℓ 2 (Z Z p) can be obtained. Moreover, a redefinition of the dilation operator on ℓ 2 (Z Z p) directly yields an algorithmic structure similar to that appearing with multiresolution analyses.
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Kristin Flornes, Alex Grossmann, Matthias Holschneider, Bruno Torrésani. Wavelets on Discrete Fields. Applied and Computational Harmonic Analysis, Elsevier, 1994, ⟨10.1006/acha.1994.1001⟩. ⟨hal-01221478⟩

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