Paley-Wiener-Schwartz nearly Parseval frames on noncompact symmetric spaces. (English) Zbl 1322.43009
Mayeli, Azita (ed.) et al., Commutative and noncommutative harmonic analysis and applications. AMS special session in memory of Daryl Geller on wavelet and frame theoretic methods in harmonic analysis and partial differential equations, Rochester, NY, USA, September 22–23, 2012. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-9493-4/pbk; 978-1-4704-1106-0/ebook). Contemporary Mathematics 603, 55-71 (2013).
Summary: 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.
For the entire collection see [Zbl 1278.00026].
For the entire collection see [Zbl 1278.00026].
MSC:
| 43A85 | Harmonic analysis on homogeneous spaces |
| 41A17 | Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities) |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 41A10 | Approximation by polynomials |
| 42C15 | General harmonic expansions, frames |
