An Anisotropic Balian-Low Phenomenon: Geometric Obstructions to Wavelet Frames
Classical Analysis and ODEs
2026-05-26 v2 Functional Analysis
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.
Keywords
Cite
@article{arxiv.2601.01821,
title = {An Anisotropic Balian-Low Phenomenon: Geometric Obstructions to Wavelet Frames},
author = {Kai-Cheng Wang},
journal= {arXiv preprint arXiv:2601.01821},
year = {2026}
}