# On a Polyconvolution with a Weight Function for Fourier Cosine and Laplace Transforms

01 Dec 2016-Vol. 41, Iss: 4, pp 549-562

TL;DR: In this paper, the generalized convolution with a weight function for the Hartley and Fourier cosine transforms is introduced, and several algebraic properties and applications of this generalized convolutions to solving a class of integral equations of Toeplitz plus Hankel type and a general class of systems of integral equation are presented.

Abstract: In this paper, we introduce the generalized convolution with a weight function for the Hartley and Fourier cosine transforms. Several algebraic properties and applications of this generalized convolution to solving a class of integral equations of Toeplitz plus Hankel type and a class of systems of integral equations are presented.

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TL;DR: In this article, a convolution of the Hankel transform is constructed for the calculation of an integral containing Bessel functions of the first kind, and the convolution is used to calculate an integral of the form

Abstract: In the paper a convolution of the Hankel transform is constructed. The convolution is used to the calculation of an integral containing Bessel functions of the first kind.

27 citations

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TL;DR: In this paper, a generalized convolution with a weight function for the Fourier cosine and sine transforms is introduced, and its properties and applications to solving a system of integral equations are considered.

Abstract: A generalized convolution with a weight function for the Fourier cosine and sine transforms is introduced. Its properties and applications to solving a system of integral equations are considered.

22 citations

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TL;DR: The generalized convolution with a weight function for the Fourier sine and cosine transforms is introduced in this paper, and its properties and applications to solving system of integral equations are considered.

Abstract: The generalized convolution with a weight function for the Fourier sine and cosine transforms is introduced. Its properties and applications to solving system of integral equations are considered.

21 citations