Frames for spaces of Paley-Wiener functions on Riemannian manifolds
Functional Analysis
2011-04-12 v1 Spectral Theory
Abstract
It is shown that Paley-Wiener functions on Riemannian manifolds of bounded geometry can be reconstructed in a stable way from some countable sets of their inner products with certain distributions of compact support. A reconstruction method in terms of frames is given which is a generalization of the classical result of Duffin-Schaeffer about exponential frames on intervals. All results are specified in the case of the two-dimensional hyperbolic space in its Poincare upper half-plane realization.
Keywords
Cite
@article{arxiv.1104.1710,
title = {Frames for spaces of Paley-Wiener functions on Riemannian manifolds},
author = {Isaac Pesenson},
journal= {arXiv preprint arXiv:1104.1710},
year = {2011}
}
Comments
Integral geometry and tomography, 135-148, Contemp. Math., 405, Amer. Math. Soc., Providence, RI, 2006