Iterated Stieltjes transform of generalized functions

L. S. Dube

International Journal of Mathematics and Mathematical Sciences, 1985, vol. 8, 1-8

Abstract:

The generalized S 2 -transform of a member of f of a certain space of generalized functions is defined as F ( x ) = 〈 f ( t ) , k ( x , t ; ρ ) 〉 , where k ( x , t ; ρ ) = ∫ 0 ∞ 1 ( x + y ) ρ ( y + t ) ρ d y , ρ > 1 2 , 0 < x < ∞ and 0 < t < ∞ . An inversion theorem for the transform is established interpreting the oonvergene in the weak distributional sense.

Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:928365

DOI: 10.1155/S0161171285000461

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