A Sharp Balian-Low Uncertainty Principle for Shift-Invariant Spaces

Douglas P. Hardin, Michael C. Northington V., Alexander M. Powell

A sharp version of the Balian-Low theorem is proven for the generators of finitely generated shift-invariant spaces. If generators $\{f_k{\}}_{k=1}^K\subset L^2({\mathbb{R}}^d)$ are t…