Paley-Wiener properties for spaces of entire functions

Abstract

We deduce Paley-Wiener results in the Bargmann setting, which give characterisations of Pilipovi{ć} spaces of low orders, extending the characterisation of a Gr{ö}chenig test function space, deduced earlier by the third author.

32 pages. Comments to 2nd version: A thorough revision has been performed. For example, complete reorganisations and reformulations of the results and main investigations in Section 2 have been performed. Hopefully the new style will be more attractive for the reader. Comments to 3-4rd versions: Some mistakes have been corrected. Section 3 added and concerns characterizations of Pilipovic spaces