On the Calder\'on sum formula for wavelet systems
Classical Analysis and ODEs
2026-02-12 v1 Functional Analysis
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.
Cite
@article{arxiv.2602.10766,
title = {On the Calder\'on sum formula for wavelet systems},
author = {Ulrik Enstad and Jordy Timo van Velthoven},
journal= {arXiv preprint arXiv:2602.10766},
year = {2026}
}
Comments
12 pages