Paley–Wiener properties for spaces of power series expansions

Abstract

We extend Paley-Wiener results in the Bargmann setting deduced in [8] to larger class of power series expansions. At the same time we deduce characterisations of all Pilipović spaces and their distributions (and not only of low orders as in [8]).( 0.1) The latter equality in (0.1) is in [8] refined into the relationfor some characteristic function χ of a polydisc D, centered at origin, and a function F which is defined and analytic in a neighbourhood of D. The spaces A 0,♭ 1 (C d ) is also characterized in [8] by2010 Mathematics Subject Classification. primary 46F05; 32A25; 32A36; secondary 35Q40; 30Gxx.