## Frame decomposition of smoothness spaces

- Nov. 9, 2006
- 3:30 p.m.
- LeConte 312

## Abstract

In applicable harmonic analysis, smoothness space are often designed following the principle that smoothness should be characterized by (or at least imply) some decay or sparseness of an associated discrete expansion. For example, sparse orthonormal wavelet expansions correspond to smoothness measured in a Besov space.

In this talk we consider a large class of smoothness spaces on R^d of so-called decomposition type for which adapted tight frames for L_2 can be constructed. The smoothness norm can be completely characterized by a sparseness condition on the frame coefficients.