Characterization of Banach-space-valued functions involving the Weinstein transform

Abstract

In this paper, the space H(A) is defined by exploiting the theory of the Weinstein transform, and proved that Weinstein transform Fw (ϕ) is an automorphism on the space H(A). The Banach space-valued test functions of Beurling type ultradistribution Hω (A) is defined by taking the weight function ω. It is shown that the subspace DR n+1(A) is dense inHω(A) and the Weinstein transform Fw (ϕ) is an automorphism + on the space Hω (A). Further showed that the linear space ωDR n+1(A) ⊕ (A) is dense inHω(A). + © 2025, University of Nis. All rights reserved.