### Sharp Uncertainty Principles for Shift-Invariant Spaces

- Series
- Analysis Seminar
- Time
- Wednesday, November 11, 2015 - 14:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Michael Northington – Vanderbilt University – michael.c.northington.v@vanderbilt.edu

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 which prevent these spaces from being invariant under
any non-integer shifts.