Frames for spaces of Paley-Wiener functions on Riemannian manifolds

Details Frames for spaces of Paley-Wiener functions on Riemannian manifolds Frames for spaces of Paley-Wiener functions on Riemannian manifolds

2011-04-09

arxiv.org/abs/1104.1710v1

Mathematics

Functional Analysis

Integral geometry and tomography, 135-148, Contemp. Math., 405, Amer. Math. Soc., Providence, RI, 2006

Scientific paper

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.

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