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arXiv · 2609.08746

Wavelet orthonormal bases for nonexpansive dilations

Jordy Timo van Velthoven·Felix Voigtlaender
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Abstract

We construct wavelet orthonormal bases for nonexpansive dilations and integer translations that do not admit a wavelet set. In addition, these orthonormal bases do not satisfy the Calder\'on sum formula. In particular, we show the existence of a wavelet basis for a dilation matrix with determinant one.

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Jordy Timo van Velthoven, Felix Voigtlaender. 2026-09-08. Wavelet orthonormal bases for nonexpansive dilations. https://arxiv.org/abs/2609.08746

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