Event Type:

Analysis Seminar

Date/Time:

Monday, May 4, 2015 - 12:00 to 13:00

Location:

BAT 250

Guest Speaker:

Institution:

University of Oregon

Abstract:

A famous theorem of Wiener uses the Fourier transform to describe the subspaces of L^2(R) invariant under translation by all real numbers. In the modern theory of wavelets and Gabor systems, we often want a weaker condition: invariance under translaton by _integers_. We give a new classification of such spaces using the Zak transform, a kind of partial Fourier transform for L^2(R) that uses the group structure of Z instead of R. This technique generalizes to the setting of abstract harmonic analysis. If G is any second countable locally compact group with a closed abelian subgroup H, we introduce a notion of Zak transform that can be used to classify the subspaces of L^2(G) invariant under left translations by H. If time permits, we will describe some applications in the theory of frames generated by abelian group actions.