Wednesday, May 8th, 2013
2:00pm - 3:00pm, in McCormack 2-116

Jens Christensen

Tufts University

Decomposition of Banach spaces via wavelet transforms

Abstract: Wavelets have been used in the image compression standard JPEG2000; the FBI uses them for fingerprint storage, and they have also be applied in image de-noising. In this talk I will explore some of the mathematics behind wavelets and their extensions. I will start with a quick tour of the history and applications of wavelets in order to motivate the study of generalizations. We then move on to continuous wavelets and see how atomic decompositions in both Hilbert and Banach spaces can be obtained via sampling of the wavelet transform. We will finish by obtaining a decomposition of Besov spaces related to symmetric cones via this theory, and I will propose extensions to these results.