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On One Integral Representation of Solutions of Polyharmonic Equation
AbstractIn the paper, an elementary solution of polyharmonic equation is determined and, with the help of it, an integral representation of solutions...
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Approximate solution of Volterra-Fredholm integral equations using generalized barycentric rational interpolant
It is well-known that interpolation by rational functions results in a more accurate approximation than the polynomials interpolation. However,...
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Spectral decomposition of Dunkl Laplacian and application to a radial integral representation for the Dunkl kernel
For the Dunkl Laplacian associated with a Coxeter group, the Von Neumann spectral decomposition is given. As a consequence, for the Dunkl kernel an...
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Representation of Weierstrass integral via Poisson integrals
In our research, we have presented a second-order linear partial differential equation in polar coordinates. Considering this differential equation...
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Integral Equations and Integral Transforms
This comprehensive textbook on linear integral equations and integral transforms is aimed at senior undergraduate and graduate students of...
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Asymptotic Behavior of the Solution for One Class of Nonlinear Integral Equations of Hammerstein Type on the Whole Axis
A class of nonlinear integral equations on the whole axis with a noncompact integral operator of Hammerstein type is investigated. This class of...
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Wavelet representation of singular integral operators
This article develops a novel approach to the representation of singular integral operators of Calderón–Zygmund type in terms of continuous model...
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Features of the Application of Integral Transformations to the Solution of Some Wave Problems
The solution of wave problems is usually connected with significant difficulties. One of the effective methods for solving these problems is the...
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Uniqueness of a Solution to the Lavrent’ev Integral Equation in n-Dimensional Space
AbstractWe study the multidimensional analogue of the Lavrent’ev integral equation to which an inverse problem of acoustic sounding is reduced....
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Determination of Stresses in an Anisotropic Strip with Holes by Using Singular Integral Equations and Green’s Solution
By the method of successive approximations (Schwartz algorithm) and the Fourier integral transform, we construct a Green-type solution for an...
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Analytical Representation of the Integral Scattering Cross-Section in the Integrofunctional Discrete Source Method
AbstractAn analytical expression is obtained for the total scattering cross-section in the discrete source method, which uses the representation of...
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Numerical Construction of the Transform of the Kernel of the Integral Representation of the Poincaré–Steklov Operator for an Elastic Strip
AbstractFor an isotropic stratified elastic strip we consider the Poincaré–Steklov operator that maps normal stresses into normal displacements on...
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An integral equation representation for American better-of option on two underlying assets
In this paper, we study the problem for pricing of American better-of option on two assets. Due to two correlated underlying assets and...
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Approximate solution of Cauchy integral equations by using Lucas polynomials
This article researches the approach to solving different instances of Cauchy integral equations by utilizing the Lucas polynomial technique. The...
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Nonlocal Balance Equation: Representation and Approximation of Solution
We study a nonlocal balance equation that describes the evolution of a system consisting of infinitely many identical particles those move along a...
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Construction of Integral Representations of Fields in Problems of Diffraction by Penetrable Bodies of Revolution
AbstractBased on integral representations with densities distributed along a segment of the symmetry axis, a representation of the solution of the...
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Convergence of the Projection-Difference Method for the Approximate Solution of a Smoothly Solvable Parabolic Equation with a Weighted Integral Condition
We search for an approximate solution of an abstract linear parabolic equation in a Hilbert space with a nonlocal weighted integral condition by the...
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Numerical Solution of a Weakly Singular Integral Equation by the Method of Orthogonal Polynomials in Various Function Classes
AbstractWe consider a singular integral equation with a logarithmic singularity that is used in the mathematical model of the scattering of...
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Integral Representations for Second-Order Elliptic Systems in the Plane
AbstractA fundamental solution matrix for elliptic systems of the second order with constant leading coefficients is constructed. It is used to...