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Singular integral equations with multiplicative Cauchy-type kernels

Kaczmarek P., Pylak D., Wójcik P.

Fasciculi Mathematici

2013

Nr 50

77--90

In this paper we consider singular integral equations of the first kind with multiplicative Cauchy-type kernels defined on n-dimensional domains. We give their general solutions in the class of Holder continuous functions and propose the statements of uniqueness problem.

Singular integral equation with a multiplicative Cauchy kernel in the half-plane

Karczmarek P.

Opuscula Mathematica

2008

Vol. 28, no. 1

63-72

In this paper the explicit solutions of singular integral equation with a multiplicative Cauchy kernel in the half-plane are presented.

Approximate solutions of a singular integral equation with Cauchy kernels in the quarter plane

Pylak D.

Opuscula Mathematica

2008

Vol. 28, no. 2

179-194

In the paper, we present explicit formulae for the solution of the singular integral equation with Cauchy kernels in the quarter plane. Next, Jacobi and Chebyshev polynomials are used to derive approximate solutions of this equation.

Application of Chebyshew and trigonometric polynomials to the approximation of a solution of a singular integral equation with a multiplicative Cauchy kernel in the half-plane

Karczmarek P.

Opuscula Mathematica

2008

Vol. 28, no. 2

129-136

In this article Chebyshev and trigonometric polynomials are used to construct an approximate solution of a singular integral equation with a multiplicative Cauchy kernel in the half-plane.