# This Week's Colloquium and Seminars

November 18- November 22, 2013

### Math Department Colloquium

Friday, November 22, 4:00-5:00 p.m. in DU 348
Speaker:  Ben Robinson, Arizona State University
Title:   Operator-valued Frames in Harmonic Analysis

Abstract: In this talk, we introduce the concept of a frame, which has received much attention in the last three decades in the sensing community and other places. A kind of overcomplete orthonormal basis, a frame is a way of collecting scalar data from a function and doing a reconstruction from that data. Recently, several authors have noted that the concept of a frame extends easily the collection of vector-valued data, an extension which may have applications to distributed sensing problems in $L^2(R^n)$. We show that these operator-valued frames arise again in a natural way from the analysis of $L^2(K)$, where $K$ is a compact subset of a Lie group $G$, providing a natural way to decompose compactly supported signals on $G$. Further, we show that for some groups, in particular the Heisenberg group and the Euclidean motion groups, there is a great deal of laxity in the choice of operators that make an operator-valued frame.

Coffee and refreshments at 3:30 in Watson 322