English

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

R2 v1 2026-06-22T02:22:24.483Z