Abelian and Parseval-Goldstein Theorems for the Kontorovich-Lebedev-Clifford Transform in Spaces of Distributions and Generalized Functions

This work 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.