**Time: ** Tuesday, February 16, 2016

2:00pm

MTH3206

**Speaker: **Michael Northington V (Vanderbilt University)

**Title: **Sharp Balian-Low Type Theorems for Shift-Invariant Spaces

**Abstract: **
Uncertainty principles are results which restrict the localization of a function and its Fourier transform. One class of uncertainty principles studies generators of structured systems of functions, such as wavelets or Gabor systems, under the assumption that these systems form a basis or some generalization of a basis. An example is the Balian-Low Theorem for Gabor systems. In this talk, I will discuss sharp, Balian-Low type, uncertainty principles for finitely generated shift-invariant subspaces of $L^2(\R^d)$. In particular, we give conditions on the localization of the generators and the type of “basis” formed by integer translates of the generators, which prevent these spaces from being invariant under any non-integer shifts.