Abstract
In this paper, we introduce a generalized Stockwell transform on a class of locally compact non-abelian groups represented as semidirect products. Specifically, let [Formula: see text], where [Formula: see text] and [Formula: see text] are locally compact groups, [Formula: see text] is abelian, and [Formula: see text] is a continuous homomorphism. For a fixed window function [Formula: see text], we define the Stockwell transform [Formula: see text] associated with this group structure. We provide an explicit inversion formula, highlighting the practical computability of the transform. Furthermore, we demonstrate that the range of [Formula: see text] forms a reproducing kernel Hilbert space and establish necessary and sufficient conditions for its surjectivity.