On an Integral Equation with the Riemann Function Kernel
This paper is concerned with a study of a special integral equation. This integral equation arises in many applied problems, including transmutation theory, inverse scattering problems, the solution of singular Sturm–Liouville and Shrödinger equations ...
Sergei Sitnik, Abdul Ahad Arian
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An explicit kernel-split panel-based Nystr\"om scheme for integral equations on axially symmetric surfaces [PDF]
A high-order accurate, explicit kernel-split, panel-based, Fourier-Nystr\"om discretization scheme is developed for integral equations associated with the Helmholtz equation in axially symmetric domains.
Helsing, Johan, Karlsson, Anders
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Commutators of singular integrals revisited [PDF]
We obtain a Bloom-type characterization of the two-weighted boundedness of iterated commutators of singular integrals. The necessity is established for a rather wide class of operators, providing a new result even in the unweighted setting for the first order commutators.
Lerner, Andrei+2 more
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OPERATOR METHOD IN THE PROBLEM OF THE H-POLARIZED WAVE DIFFRACTION BY TWO SEMI-INFINITE GRATINGS PLACED IN THE SAME PLANE [PDF]
Purpose: Problem of the H-polarized plane wave diffraction by the structure, which consists of two semi-infinite strip gratings, is considered. The gratings are placed in the same plane. The gap between the gratings is arbitrary. The purpose of the paper
M. E. Kaliberda+2 more
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Approximate methods for solving degenerate singular integral equations
Background. Singular integral equations in degenerate cases describe many processes in natural science and technology. The theory of these equations has been studied quite well, but as far as the authors know, there are currently no analytical methods ...
Il'ya V. Boykov, Anastasiya A. Pivkina
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Rank one perturbations and singular integral operators [PDF]
We consider rank one perturbations $A_\alpha=A+\alpha(\cdot,\varphi)\varphi$ of a self-adjoint operator $A$ with cyclic vector $\varphi\in\mathcal H_{-1}(A)$ on a Hilbert space $\mathcal H$. The spectral representation of the perturbed operator $A_\alpha$
Liaw, Constanze, Treil, Sergei
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Boundedness for a Class of Singular Integral Operators on Both Classical and Product Hardy Spaces
We found that the classical Calderón-Zygmund singular integral operators are bounded on both the classical Hardy spaces and the product Hardy spaces. The purpose of this paper is to extend this result to a more general class. More precisely, we introduce
Chaoqiang Tan
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Excited States of Calogero-Sutherland Model and Singular Vectors of the $W_N$ Algebra [PDF]
Using the collective field method, we find a relation between the Jack symmetric polynomials, which describe the excited states of the Calogero-Sutherland model, and the singular vectors of the $W_N$ algebra.
Avan+49 more
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Investigation on the Singularities of Some Singular Integrals
In a boundary element method, the treatment of all the possible singular integrals is very important for the correctness and accuracy of the solutions. Generally, the directional derivative of a weakly singular integral is computed by an integral in the sense of Cauchy principal value if the directional derivative of the weakly singular integral kernel
Qiang Zhang, Zai You Yan
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A Regularization of Fredholm type singular integral equations
We present a method to regularize first and second kind integral equations of Fredholm type with singular kernel. By appropriate application of the Poincaré-Bertrand formula we change such integral equations into a second kind Fredholm's integral ...
N. Aliev, S. Mohammad Hosseini
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