Relations between Hermite and Laguerre expansions of ultradistributions over R d and R + d

Abstract

The aim of this paper is twofold. Firstly, to show the existence of topological isomorphism between the G-type spaces G(alpha)(alpha) (R-+(d)), alpha gt = 1 and the subspaces of the Gelfand-Shilov spaces S-alpha/2 (alpha/2) (Rd), alpha gt = 1, consisting of "even" functions. The same is done for their dual spaces. Secondly, to obtain two structural theorems for the dual spaces (G(alpha)(alpha)(R-+(d)))', alpha gt = 1.