# Analysis Seminar

## Wednesday, 22 January, 2014

**SPEAKER: **Prof. Mike Frazier, UTK

**TITLE: *** **Traces of Function Spaces via Atomic Decompositions*

**ABSTRACT: **For some space X of functions on R^n, we consider when it is possible to define the trace, or restriction, of each element of X to any n-1 dimensional hyperplane, which we identify with R^{n-1}. If X is a Sobolev space W^{k,p}, with 1<p<infty, the trace of W^{k,p} is a certain Besov space.

The same Besov space is also the trace of another Besov space with higher index. We consider the trace problem from the standpoint of wavelet-like atomic decompositions coming from Littlewood-Paley theory. We obtain a geometric explanation of these trace results, including the anomaly that different spaces on R^n have the same trace space.

## Cost

Free## Event Contact

Betty MorganPhone: 974-2463