On a polyconvolution with a weight function for Fourier cosine and Laplace transforms
type: Item
instance of: scholarly article
title: On a polyconvolution with a weight function for Fourier cosine and Laplace transforms
zbMATH Open document ID: 1360.44007
published in: Acta Mathematica Vietnamica
publication date: 2017-01-26T00:00:00Z
review text: Convolutions and generalized convolutions have remained common nomenclatures with several investigations related with the integral transforms and their applications in science and mathematics. A general definition of polyconvolution was proposed by \textit{V. A. Kakichev} [in: Mathematical modelling and complex analysis. Proceedings of the 2nd international conference, Vilnius, Lithuania, June 3--4, 1997. Vilnius: Technika. 79--83 (1997; Zbl 0963.44500)] for \((n+1)\) arbitrary integral transforms with certain weight function of functions for which the factorization property holds true. This notion is found to have been applied to integral transforms, viz. Fourier, Fourier cosine, Fourier sine, or Hartley and types of Fourier transforms (citations of such applications can be seen in the current paper, under review). The present paper claims to have studied a new polyconvolutions with a weight function for the Fourier cosine and Laplace transform and proves the existence of the same in certain function spaces, and also includes the proofs of the same for the factorization equality and algebraic properties (one may refer to Theorems 3.2-- 3.4 in Section 3). Boundedness of polyconvolution under certain prescribed conditions is obtained in Section 4, even one can notice Equation (13) in this context. Integral transforms related to this polyconvolution are studied in Section 5. A class of Toeplitz-Hankel integral equations and certain systems of integral equations are studied by virtue of the polyconvolution (proposed in the present paper) and it is proved that these equations can be solved in a closed form in Section 6.
reviewed by: Deshna Loonker
Mathematics Subject Classification ID: 44A35
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 42A38
Mathematics Subject Classification ID: 44A10
zbMATH DE Number: 6678128
zbMATH Keywords: convolution
zbMATH Keywords: polyconvolution
zbMATH Keywords: generalized convolution
zbMATH Keywords: Fourier transform
zbMATH Keywords: Fourier sine transform
zbMATH Keywords: Fourier cosine transform
zbMATH Keywords: Hartley transform
zbMATH Keywords: Toeplitz-Hankel integral equation
author: Nguyen Minh Khoa
MaRDI profile type: Publication
full work available at URL: s40306-015-0154-8
OpenAlex ID: W1861543814
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DOI: 10.1007/S40306-015-0154-8
description: scientific article; zbMATH DE number 6678128