Results 271 to 280 of about 11,165 (303)

Logarithmic functions are eigenfunctions of integral operators with M-Wright kernels

Journal of Computational and Applied Mathematics, 2021
Let \[M_{\beta } (z)=\sum _{n=0}^{\infty }\frac{(-1)^{n} z^{n} }{n!\Gamma (-\beta n+1-\beta )} \quad ...
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Criteria for the Boundedness and Compactness of Operators with Power-Logarithmic Kernels

Analysis Mathematica, 2001
Consider numbers \(10\) and \(a>0\). The authors consider the operator \(I_{\alpha,\beta}\) defined on \(L^p(0,a)\) by \[ I_{\alpha,\beta}f(x)=\int_0^x(x-t)^{\alpha-1}\ln^\beta(\gamma/(x-t))f(t) dt. \] They show that this operator is bounded from \(L^p(0,a)\) to \(L^q(0,a;\nu)\) (here \(\nu\) is a finite Borel measure on \((0,a)\)) if and only if the ...
Kokilashvili, V., Meskhi, A.
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A Simplified Procedure for Singular Integral Equations with Logarithmic Kernels

IMA Journal of Applied Mathematics, 1970
An exact construction of solutions to a class of singular integral equations given by Morland (1970) is approximated to reduce computer storage and time. Applications are to kernels which are the sum of a continuous bounded function and a logarithm multiplied by a second continuous bounded function, with the possible addition of a strong singularity ...
Margetson, J., Morland, L. W.
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Singular integral equations with logarithmic kernels

Mathematika, 1970
Closed form solutions are obtained for a class of singular integral equations of the first kind with difference kernels. The kernel function is the sum of a polynomial and a second polynomial multiplied by a logarithm, with the possible addition of a strong singularity. A wider class of kernels have approximate representations in one of the above forms,
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Diffusion Kernels of Logarithmic Type

1988
Let X be a locally compact, non-compact Hausdorff space with countable basis. We denote by: CK(X) the usual topological vector space of all finite continuous functions with compact support; C(X) the usual Frechet space of all finite continuous functions on X; MK(X) the usual topological vector space of all real Radon measures with ...
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Mellin Transform and Integro-Differential Equations with Logarithmic Singularity in the Kernel

Lobachevskii Journal of Mathematics, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yuldashev, T. K., Zarifzoda, S. K.
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Mesh Grading for Integral Equations of the First Kind with Logarithmic Kernel

SIAM Journal on Numerical Analysis, 1989
Galerkin's method is to be used to solve a Fredholm integral equation of the first kind in which the kernel has a logarithmic singularity, and the path of integration is either a polygon or an open arc. The singularities of the solution, due to corners of the boundary or end points of the arc, will adversely affect the rate of convergence of the ...
Yan, Y., Sloan, I. H.
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Quadratic numerical treatment for singular integral equations with logarithmic kernel

International Journal of Computing Science and Mathematics, 2019
The goal of this paper is to present a direct method for an approximative solution of a weakly singular integral equations (WSIE) with logarithmic kernel on a piecewise smooth integration path using a modified quadratic spline approximation, we also show that this approximation gives an efficient approach to the analytical solution of WSIE.
Mostefa Nadir, Bachir Gagui
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Numerical solution of an integral equation with a logarithmic kernel

BIT, 1971
When formulating boundary value problems within different branches of mathematical physics, one encounters an integral equation whose kernel is equal to the logarithm of the distance between two points on a plane, closed, smooth, and simple curve. This equation can be replaced by a system of linear algebraic equations which can be solved numerically.
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Optimal approximation of operators with power-logarithmic kernels

Uzbek Mathematical Journal
This paper presents the construction of an optimal quadrature formula in the Sobolev space L(m)2 (0; x) for integrals with power-logarithmic kernels. Formulas for calculating the coefficients of the optimal quadrature formula are derived. An example is considered to validate the optimal quadrature formula.
Kh.M. Shadimetov, Kh.I. Usmanov
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