On the iterated Stieltjes transform and its convolution with applications to singular integral equations

DOI10.1080/10652469.2013.868457zbMath1348.44004arXiv1311.3084OpenAlexW2217478276MaRDI QIDQ5404148

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Publication date: 21 March 2014

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.3084

zbMATH Keywords

Laplace transformMellin transformsingular integral equationsHilbert transformconvolution methoditerated Stieltjes transformTitchmarsh theorem

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Laplace transform (44A10) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Integral equations with kernels of Cauchy type (45E05)

Related Items (5)

Iteration of the Laplace transform over generalized functions and a Post-Widder inversion formula over distributions of compact support ⋮ Theorems connecting Stieltjes transform and Hankel transform ⋮ On the half-Hartley transform, its iteration and compositions with Fourier transforms ⋮ The Markov–Stieltjes transform on Hardy and Lebesgue spaces ⋮ On the generalized Hurwitz-Lerch zeta function and generalized Lambert transform

Cites Work

• An inversion of the \(S_2\) transform for generalized functions
• A new convolution theorem for the Stieltjes transform and its application to a class of singular integral equations

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