The Weinstein transform associated with a family of generalized distributions

Abstract

Recently, Björck (Ark Mat 6:351–407, 1966) and Hörmander (Linear Partial Differential Operators, vol 116, Springer, Berlin, 1963) investigated the linear partial differential operators and generalized distributions, which are associated with the Fourier transform, by utilizing the convolution properties on spaces of the types Dω(Rn) , Eω(Rn) and Sω(Rn) . Motivated essentially by the above-cited developments, the present paper examines various properties of the Weinstein transform over the generalized distributions Dω′(R+n+1) and other spaces. The convolution properties of the generalized distributions, which are associated with the Weinstein transform on the space Dω′(R+n+1), are also discussed herein. © 2023, The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid.