On the Calder\'on sum formula for wavelet systems
Ulrik Enstad, Jordy Timo van Velthoven
TL;DR
This paper proves that the Calderón sum formula applies to orthonormal wavelet bases with arbitrary dilation and translation matrices, under mild conditions, advancing understanding of wavelet theory.
Contribution
It demonstrates that the Calderón sum formula holds for a broader class of wavelet systems, partially resolving a conjecture by Bownik and Lemvig.
Findings
Calderón sum formula holds for arbitrary dilation and translation matrices.
The result applies under mild conditions on the wavelet function.
Partial resolution of a conjecture by Bownik and Lemvig.
Abstract
We show that the Calder\'on sum formula for orthonormal wavelet bases holds for arbitrary dilation and translation matrices under a mild condition on the wavelet function. This partially solves a conjecture by Bownik and Lemvig.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Image and Signal Denoising Methods · Holomorphic and Operator Theory