Banach-Space-Valued Ultradistributions Involving the Weinstein Transform

Abstract

The Weinstein transform theory is utilized in this study to define the space H(A) and demonstrates that the 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 explained by adopting the weight function ω. The subspace Dℝ(A) is shown to be dense in Hω(A) and the Weinstein transform ℱw(ϕ) is an automorphism on the space Hω(A). Furthermore, it is also shown in the paper that the linear space omega upper D Subscript double struck upper R Sub Subscript plus Sub Superscript n plus 1 Baseline left parenthesis upper A right parenthesis circled asterisk left parenthesis upper A right parenthesis) is dense in Hω(A). © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.