Continuous Framings for Banach Spaces

Release:2017-03-17 Viewed:26


Lecturer:Prof Pengtong Li

Time    24 March  Friday 1600-1700

Place   : Classroom 7th

Theme   Continuous Framings for Banach Spaces

Abstract:The theory of discrete and continuous frames was introduced for the purpose of analyzing and reconstructing signals mainly in Hilbert spaces. However, in many interesting applications the analyzed space is usually a Banach space, and consequently the stable analysis/reconstruction schemes need to be investigated for general Banach spaces. Parallel to discrete Hilbert space frames, the theory of atomic decompositions, p-frames and framings have been introduced in the literature to address this problem. In this paper, we focus on continuous frames / continuous framings (alternatively, integral reconstructions) for Banach spaces by the means of g-Kothe function spaces. Necessary and sufficient conditions for a measurable function to be a continuous frame are obtained, and we obtain a decomposition result for the analysis operators of continuous frames in terms of simple Kothe-Bochner operators. As a byproduct, we show that a Riesz type continuous frame does not exist unless the associated measure space is purely atomic. One of our main results shows that there is an intrinsic connection between continuous framings and g-Kothe function spaces. (Joint with Fengjie Li and Deguang Han)