Paley-Wiener description of K-spherical Besov spaces on the Heisenberg group

Abstract

We characterize the Besov spaces associated to the Gelfand pairs on the Heisenberg group. The characterization is given in terms of bandlimited wavelet coefficients where the bandlimitedness is introduced using spherical Fourier transform. To obtain these results we develop an approach to the characterization of Besov spaces in abstract Hilbert spaces through compactly supported admissible functions.