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arXiv · 2601.01821

An Anisotropic Balian-Low Phenomenon: Geometric Obstructions to Wavelet Frames

Kai-Cheng Wang
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Abstract

We investigate the analytic stability of wavelet frames in anisotropic Hardy spaces associated with expansive dilation matrices. The main result establishes a deterministic operator-norm lower bound on the reconstruction error of the mixed frame operator, uniformly across the Hardy range, whenever a real eigenvalue of the adjoint dilation exceeds a band-limited threshold imposed on a radial generator. The obstruction is identified as an anisotropic Balian--Low phenomenon and rests on a geometric incompatibility index measuring the deviation of the Calder\'{o}n sum from the admissibility identity. The bound carries no dependence on the conditioning of the dilation.

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BibTeXRIS

Kai-Cheng Wang. 2026-01-05. An Anisotropic Balian-Low Phenomenon: Geometric Obstructions to Wavelet Frames. https://arxiv.org/abs/2601.01821

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