Shannon Sampling and Parseval Frames on Compact Manifolds

2013/12/06 by Isaac Z. Pesenson, Pesenson, Isaac Z.
Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Information Theory (cs.IT) #cs.IT #math.FA #math.IT

paper · pdf · doi:10.48550/arxiv.1312.1882

Delivered during Sampta 2013 in Jacobs University in Bremen

arxiv created 2013/12/06 · arxiv updated 2013/12/09

Abstract

Our article is a summary of some results for Riemannian manifolds that were obtained in \citegpes-\citePesssubm. To the best of our knowledge these are the pioneering papers which contain the most general results about frames, Shannon sampling, and cubature formulas on compact and non-compact Riemannian manifolds. In particular, the paper \citegpes gives an "end point" construction of tight localized frames on homogeneous compact manifolds. The paper \citePessubm is the first systematic development of localized frames on compact domains in Euclidean spaces.

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