Abelian and Parseval-Goldstein theorems for the Kontorovich-Lebedev-Clifford transform in spaces of distributions and generalized functions

This paper is devoted to the study of the Kontorovich-Lebedev-Clifford transform (KLC-transform). We establish Abelian theorems for the KLC-transform in two distinct settings: distributions with compact support, and certain spaces of generalized functions. Furthermore, a significant portion of the paper is dedicated to deriving Parseval-Goldstein type theorems for the KLC-transform, highlighting structural and duality properties of the transform and its adjoint.