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

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.

published in "Commutative and Noncommutative Harmonic Analysis and Applications", Contemporary Mathematics, v. 603, (2013), pp.55-73. arXiv admin note: text overlap with arXiv:1104.1711