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arXiv · 1308.1893

Paley-Wiener-Schwartz nearly Parseval frames and Besov spaces on noncompact symmetric spaces

Isaac Z. Pesenson
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Abstract

Let $X$ be a symmetric space of the noncompact type. The goal of the paper is to construct in the space $L_{2}(X)$ nearly Parseval frames consisting of functions which simultaneously belong to Paley-Wiener spaces and to Schwartz space on $X$. We call them Paley-Wiener-Schwartz frames in $L_{2}(X)$. These frames are used to characterize a family of Besov spaces on $X$. As a part of our construction we develop on $X$ the so-called average Shannon-type sampling.

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Isaac Z. Pesenson. 2014-02-08. Paley-Wiener-Schwartz nearly Parseval frames and Besov spaces on noncompact symmetric spaces. https://arxiv.org/abs/1308.1893

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