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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.

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.