English

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

R2 v1 2026-07-01T10:31:44.250Z