Shannon Sampling and Parseval Frames on Compact Manifolds
Information Theory
2013-12-09 v1 Functional Analysis
math.IT
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.
Cite
@article{arxiv.1312.1882,
title = {Shannon Sampling and Parseval Frames on Compact Manifolds},
author = {Isaac Z. Pesenson},
journal= {arXiv preprint arXiv:1312.1882},
year = {2013}
}
Comments
Delivered during Sampta 2013 in Jacobs University in Bremen