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Abelian Theorem for the Distributional Stieltjes Transform

Stevan Pilipović,Bogoljub Stanković

Zeitschrift für Analysis und ihre Anwendungen（1987）

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Abstract
We study the behaviour of the distributional Stieltjes transformation (Srf) (z), z ∈ ℂ ℝ, at zero of an f ∈ S’ which has the appropriate quasi-asymptotic behaviour at zero. By using the known results for the asymptotic behaviour at ± ∞, we obtain a final value Abelian theorem for the distributional Stieltjes transformation at zero.
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