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

摘要

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). As a part of our construction we develop on X the so-called average Shannon-type sampling.