Shannon Sampling and Parseval Frames on Compact Manifolds

Isaac Z. Pesenson

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arXiv · 1312.1882

Shannon Sampling and Parseval Frames on Compact Manifolds

Isaac Z. Pesenson

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Abstract

Our article is a summary of some results for Riemannian manifolds that were obtained in \cite{gpes}-\cite{Pesssubm}. 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 \cite{gpes} gives an "end point" construction of tight localized frames on homogeneous compact manifolds. The paper \cite{Pessubm} is the first systematic development of localized frames on compact domains in Euclidean spaces.

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Isaac Z. Pesenson. 2013-12-06. Shannon Sampling and Parseval Frames on Compact Manifolds. https://arxiv.org/abs/1312.1882

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