Groups, Operator Algebras, and Quantum Seminar

Speaker: Mahya Ghandehari (University of Delaware)

Title: Characterizing the Sobolev wavefront set via continuous wavelet transforms

Abstract: In this talk, we discuss the problem of characterizing of the Sobolev wavefront set of a tempered distribution in terms of its continuous wavelet transform, for higher dimensional continuous wavelet transforms constructed using square-integrable representations of a given semidirect product group ${\mathbb R}^n\rtimes H$ where $H$ can be any suitably chosen dilation group. Two important cases will be examined, where 1) the mother wavelet is compactly supported, and 2) the mother wavelet has compactly supported Fourier transform. This talk is based on joint work with Hartmut Fuhr.