A Comprehensive Study of Generalized Lambert, Generalized Stieltjes, and Stieltjes–Poisson Transforms

Abstract

In this paper, we explore the properties of the generalized Lambert transform, the L-transform, the generalized Stieltjes transform, and the Stieltjes–Poisson transform within the framework of Lebesgue spaces. We establish Parseval-type relations for each transform, providing a comprehensive analysis of their behaviour and mathematical characteristics.

Keywords

• generalized Lambert transform
• L-transform
• generalized Stieltjes transform
• Stieltjes–Poisson transform
• Parseval relations
• Lebesgue spaces