Twenty minutes before the talk coffee and cookies will be available in
Bear Hall 211.
Title:Frames, Uncertainty Principles and Time-Frequency
Analysis. Speaker: Mark Lammers
Abstract: A basis is a sequence of “basic functions”
or vectors that allows one to describe a large set of functions in terms
of linear combination of these more basic functions or vectors in a unique
way. The fact that this expansion is unique has long been celebrated and
exploited in mathematics. Recently however, there has been a great
deal of interest centered around types of expansion that are not unique.
One type of such an expansion is known as a frame. Along with being of great
theoretical interest in math, statistics, and physics, frames have been
shown to be a useful tool in applications such as signal denoising and digital
communication systems. I will begin by defining frames and the operators
associated with them. Next, I will present some simple examples
from non-square matrices and an elementary application in approximation theory.
In the second part of the talk I will make a connection between frames and
one of the fundamental principles in quantum mechanics known as the Heisenberg
Uncertainty Principle. Finally, I will explain how this connection
is at the heart of a modern branch of Harmonic Analysis known a Time-Frequency
This talk is intended for a very general audience and no knowledge other
than linear algebra will be assumed of those that attend.