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 F_w(phi) is an automorphism on the space H(A). The Banach space-valued test functions of Beurling type ultradistribution H_{omeg}(A) is defined by taking the weight function omega. It is
shown that the subspace D^{Rn+1}_{+}(A) is dense in H_{omga}(A) and the Weinstein transform Fw(phi) is an automorphism on the space H_{omega}(A). Further showed that the linear space omega D^{Rn+1}_{+}(A) oplus (A) is dense in H_{omrga}(A).