A Balian-Low Theorem for Subspaces

A. Caragea; D. Lee; G. E. Pfander; F. Philipp

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arXiv · 1801.09237

A Balian-Low Theorem for Subspaces

A. Caragea·D. Lee·G. E. Pfander·F. Philipp

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Abstract

We extend the Balian-Low theorem to Gabor subspaces of $L^2(\mathbb R)$ by involving the concept of additional time-frequency shift invariance. We prove that if a Gabor system on a lattice of rational density is a Riesz sequence generating a subspace which is invariant under an additional time-frequency shift, then its generator cannot decay fast simultaneously in time and frequency.

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BibTeX RIS

A. Caragea, D. Lee, G. E. Pfander, F. Philipp. 2018-01-28. A Balian-Low Theorem for Subspaces. https://arxiv.org/abs/1801.09237

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