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arXiv · 2610.18751

Methods of Construction of Exponential Bases on Planar Domains Revised

Oleg Asipchuk·Laura De Carli
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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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Oleg Asipchuk, Laura De Carli. 2026-10-13. Methods of Construction of Exponential Bases on Planar Domains Revised. https://arxiv.org/abs/2610.18751

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