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Exchange Formulae for the Stieltjes–Poisson Transform over Weighted Lebesgue Spaces
AxiomsThis paper aims to develop exchange formulae for the Stieltjes–Poisson transform by using Mellin-type convolutions in the context of weighted Lebesgue spaces. A key result is the introduction of bilinear and continuous Mellin-type convolutions, expanding
Hari M. Srivastava +2 more
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, 2013 Functional integrals are defined in terms of locally compact topological groups and their associated Banach-valued Haar integrals. This approach generalizes the functional integral scheme of Cartier and DeWitt-Morette. The definition allows a construction of functional Mellin transforms.
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AIMS MathematicsThe Mellin transform assigned to the convolution Poisson kernel on higher rank Riemannian symmetric spaces of the non-compact type is equal to the wave kernel.
Ali Hassani
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Error bound analysis and singularly perturbed Abel-Volterra equations
Journal of Applied Mathematics, 2004 Asymptotic solutions of nonlinear singularly perturbed Volterra integral equations with kernels possessing integrable singularity are investigated using singular perturbation methods and the Mellin transform technique.
Angelina M. Bijura
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On weak Mellin transforms, second degree characters and the Riemann hypothesis
, 2015 We say that a function f defined on R or Qp has a well defined weak Mellin transform (or weak zeta integral) if there exists some function $M\_f(s)$ so that we have $Mell(\phi \star f,s) = Mell(\phi,s)M\_f(s)$ for all test functions $\phi$ in $C\_c ...
Sauvalle, Bruno
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The symmetric Mellin transform in quantum calculus
Le Matematiche, 2015 In this paper, we define the q-analogue of Mellin Transform symmetric under interchange of q and 1/q, and present some of its main properties and explore the possibility of using the integral transform to solve a class of differential equations q ...
Brahim Kamel Brahim +2 more
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On the Mellin transform of a product of hypergeometric functions [PDF]
, 1998 Allen R. Miller, H. M. Srivastava
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Acta Polytechnica, 2013 The interconnection between the Cayley-Eisenstein-Pólya distribution and the Landau distribution is studied, and possibly new transform pairs for the Laplace and Mellin transform and integral expressions for the Lambert W function have been found.
Vladimír Vojta
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Analytic continuation of Mellin transforms up to two-loop order [PDF]
, 2000 J. Blümlein
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