New convolution theorem for the Stieltjes transform and its application to a class of singular integral equations

Date

2010-05-18T22:12:42Z

Authors

Srivastava, H.M.
Tuan, Vu Kim

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Abstract

A new convolution theorem is proved for the Stieltjes transform and is then applied in solving a certain class of singular integral equations which are related rather closely to the Riemann-Hilbert boundary value problem. Some further extensions and consequences of the convolution theorem are also considered.

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Keywords

convolution theorem, Stieltjes transform, singular integral equations, Riemann-Hilbert boundary value problem, Fourier transform, Laplace transform, Mellin transform, convolution integral equations, Cauchy principal values, Holder inequality, Hilbert transform, bounded operator, Riesz inequality, Lebesgue theorem, Stieltjes convolution, transcendental equation, classical inversion theorem

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