PreprintarXiv licencearXiv
Methods of Construction of Exponential Bases on Planar Domains Revised
Abstract
In [1], we surveyed classical and recent results on the construction of exponential bases on planar domains with explicit control over the associated frame bounds. We also constructed well-conditioned exponential bases on certain planar sets that multi-tile the plane. In this revision, we identify an error in the choice of basis used in the proof of Theorem 3.11 and we provide a new proof using a simpler exponential basis.
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BibTeX
@misc{asipchuk2026methods,
title = {{Methods of Construction of Exponential Bases on Planar Domains Revised}},
author = {Oleg Asipchuk and Laura De Carli},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18751},
eprint = {2610.18751},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18751},
}
RIS
TY - UNPB
TI - Methods of Construction of Exponential Bases on Planar Domains Revised
AU - Oleg Asipchuk
AU - Laura De Carli
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18751
UR - https://arxiv.org/abs/2610.18751
AB - In [1], we surveyed classical and recent results on the construction of exponential bases on planar domains with explicit control over the associated frame bounds. We also constructed well-conditioned exponential bases on certain planar sets that multi-tile the plane. In this revision, we identify an error in the choice of basis used in the proof of Theorem 3.11 and we provide a new proof using a simpler exponential basis.
ER -