Distributional Aboodh-Stieltjes Transform and its Analytical Structure

Author(s)	Prof. Dr. Aswina Rangari, Prof. Shilpa Khandekar, Prof. Dr. Vidya Sharma
Country	India
Abstract	This paper introduces a generalization of the Aboodh–Stieltjes transform in the distributional sense. Suitable testing function spaces are constructed using the Gelfand–Shilov technique to provide a rigorous framework for defining the transform on distributions. Fundamental properties of the generalized Aboodh–Stieltjes transform are investigated, and an analyticity theorem is established to describe its analytical behavior in the transform domain. The proposed approach extends the classical Aboodh–Stieltjes transform and provides a useful framework for the analysis of generalized functions and related operational problems.
Keywords	Aboodh Transform, Stieltjes Transform, Aboodh–Stieltjes Transform, Testing Function Space, Generalized function, Analyticity Theorem.
Field	Mathematics
Published In	Volume 7, Issue 5, September-October 2026
Published On	2026-09-05

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