On the Polyconvolution with the Weight Function for the Fourier Cosine, Fourier Sine, and the Kontorovich-Lebedev Integral Transforms

On the Polyconvolution with the Weight Function for the Fourier Cosine, Fourier Sine, and the Kontorovich-Lebedev Integral Transforms

The polyconvolution with the weight function γ of three functions f,g, and h for the integral transforms Fourier sine (Fs), Fourier cosine (Fc), and Kontorovich-Lebedev (Kiy), which is denoted by ∗γ(f,g,h)(x), has been constructed. This polyconvolution satisfies the following factorization propert...

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Main Author: Nguyen Xuan Thao
Format: Article
Language:English
Published: Hindawi Limited 2010-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2010/709607
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spelling doaj-4a8f5c5f9ee841958ef29c15f80b304b2020-11-24T22:36:10ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472010-01-01201010.1155/2010/709607709607On the Polyconvolution with the Weight Function for the Fourier Cosine, Fourier Sine, and the Kontorovich-Lebedev Integral TransformsNguyen Xuan Thao0Faculty of Applied Mathematics and Informatics, Hanoi University of Technology, No. 1, Dai Co Viet, Hanoi, VietnamThe polyconvolution with the weight function γ of three functions f,g, and h for the integral transforms Fourier sine (Fs), Fourier cosine (Fc), and Kontorovich-Lebedev (Kiy), which is denoted by ∗γ(f,g,h)(x), has been constructed. This polyconvolution satisfies the following factorization property Fc(∗γ(f,g,h))(y)=sin y(Fsf)(y)⋅(Fcg)(y)⋅(Kiyh)(y), for all y>0. The relation of this polyconvolution to the Fourier convolution and the Fourier cosine convolution has been obtained. Also, the relations between the polyconvolution product and others convolution product have been established. In application, we consider a class of integral equations with Toeplitz plus Hankel kernel whose solution in closed form can be obtained with the help of the new polyconvolution. An application on solving systems of integral equations is also obtained.http://dx.doi.org/10.1155/2010/709607
collection DOAJ
language English
format Article
sources DOAJ
author Nguyen Xuan Thao
spellingShingle Nguyen Xuan Thao
On the Polyconvolution with the Weight Function for the Fourier Cosine, Fourier Sine, and the Kontorovich-Lebedev Integral Transforms
Mathematical Problems in Engineering
author_facet Nguyen Xuan Thao
author_sort Nguyen Xuan Thao
title On the Polyconvolution with the Weight Function for the Fourier Cosine, Fourier Sine, and the Kontorovich-Lebedev Integral Transforms
title_short On the Polyconvolution with the Weight Function for the Fourier Cosine, Fourier Sine, and the Kontorovich-Lebedev Integral Transforms
title_full On the Polyconvolution with the Weight Function for the Fourier Cosine, Fourier Sine, and the Kontorovich-Lebedev Integral Transforms
title_fullStr On the Polyconvolution with the Weight Function for the Fourier Cosine, Fourier Sine, and the Kontorovich-Lebedev Integral Transforms
title_full_unstemmed On the Polyconvolution with the Weight Function for the Fourier Cosine, Fourier Sine, and the Kontorovich-Lebedev Integral Transforms
title_sort on the polyconvolution with the weight function for the fourier cosine, fourier sine, and the kontorovich-lebedev integral transforms
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2010-01-01
description The polyconvolution with the weight function γ of three functions f,g, and h for the integral transforms Fourier sine (Fs), Fourier cosine (Fc), and Kontorovich-Lebedev (Kiy), which is denoted by ∗γ(f,g,h)(x), has been constructed. This polyconvolution satisfies the following factorization property Fc(∗γ(f,g,h))(y)=sin y(Fsf)(y)⋅(Fcg)(y)⋅(Kiyh)(y), for all y>0. The relation of this polyconvolution to the Fourier convolution and the Fourier cosine convolution has been obtained. Also, the relations between the polyconvolution product and others convolution product have been established. In application, we consider a class of integral equations with Toeplitz plus Hankel kernel whose solution in closed form can be obtained with the help of the new polyconvolution. An application on solving systems of integral equations is also obtained.
url http://dx.doi.org/10.1155/2010/709607
work_keys_str_mv AT nguyenxuanthao onthepolyconvolutionwiththeweightfunctionforthefouriercosinefouriersineandthekontorovichlebedevintegraltransforms
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