Asymptotic analysis for complex-valued Stieltjes transforms

Abstract

Abelian theorems for complex-valued Stieltjes transforms of functions and generalized functions are obtained, which generalize all previous related results, and new results are obtained. Under limit assumptions on the function or the generalized function, the Abelian theorem results are obtained as the complex variable of the transform approaches zero or infinity within an arbitrary wedge, and in some cases arbitrarily, in the right half plane.

Keywords:

• Abelian theorems
• Stieltjes transform
• distribution

AMS Subject Classification :

• 44A15
• 46F12