Recent developments on the Stieltjes transform of generalized functions

DOI10.1155/S0161171287000784zbMath0636.46045OpenAlexW2091875246MaRDI QIDQ1098064

Lokenath Debnath, Ram Shankar Pathak

Publication date: 1987

Published in: International Journal of Mathematics and Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/46248

zbMATH Keywords

kernel methodfractional integrationGaussian hypergeometric functionAbelian theoremsmethod of adjointsiterated Stieltjes transformsreal and complex inversion theoremsrepresentation of the Stieltjes transform as iterated Laplace transformStieltjes transform of generalized functions

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Integral transforms of special functions (44A20)

Related Items (9)

A variant of the Stieltjes transform on distributions of compact support ⋮ On the generalized Stieltjes transform over weighted Lebesgue spaces and distributions of compact support ⋮ Iteration of the Laplace transform over generalized functions and a Post-Widder inversion formula over distributions of compact support ⋮ Exchange formulae for the generalized Stieltjes transform over weighted Lebesgue spaces ⋮ Finite-part integration of the generalized Stieltjes transform and its dominant asymptotic behavior for small values of the parameter. I. Integer orders ⋮ Unnamed Item ⋮ Stieltjes transforms defined by \(C_0\)-semigroups ⋮ Poisson transform on Boehmians ⋮ A distributional inversion formula for a generalization of the Stieltjes and Poisson transforms

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