PreprintarXiv licencearXiv
Wavelet orthonormal bases for nonexpansive dilations
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 Calderón sum formula. In particular, we show the existence of a wavelet basis for a dilation matrix with determinant one.
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BibTeX
@misc{velthoven2026wavelet,
title = {{Wavelet orthonormal bases for nonexpansive dilations}},
author = {Jordy Timo van Velthoven and Felix Voigtlaender},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08746},
eprint = {2609.08746},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08746},
}
RIS
TY - UNPB
TI - Wavelet orthonormal bases for nonexpansive dilations
AU - Jordy Timo van Velthoven
AU - Felix Voigtlaender
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08746
UR - https://arxiv.org/abs/2609.08746
AB - 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 Calderón sum formula. In particular, we show the existence of a wavelet basis for a dilation matrix with determinant one.
ER -