Abelian theorems for the stieltjes transform of functions, II

Richard D. Carmichael and Elmer K. Hayashi

International Journal of Mathematics and Mathematical Sciences, 1981, vol. 4, 1-22

Abstract:

An initial (final) value Abelian theorem concerning transforms of functions is a result in which known behavior of the function as its domain variable approaches zero (approaches ∞ ) is used to infer the behavior of the transform as its domain variable approaches zero (approaches ∞ ). We obtain such theorems in this paper concerning the Stieltjes transform. In our results all parameters are complex; the variable s of the transform is complex in the right half plane; and the initial (final) value Abelian theorems are obtained as | s | → 0 ( | s | → ∞ ) within an arbitrary wedge in the right half plane.

Date: 1981
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:863151

DOI: 10.1155/S0161171281000045

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