Shannon Sampling and Parseval Frames on Compact Manifolds

الأصل · EN

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