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Vietnam Journal of Mathematics 39:2 (2011) 217-235

A New Polyconvolution and Its Application to Solving

a Class of Toeplitz Plus Hankel Integral Equations

and Systems of Integral Equations

Trinh Tuan1 and Nguyen Xuan Thao2

1Department of Mathematics, Electric Power University, 235 Hoang Quoc Viet,

Hanoi, Vietnam

2Faculty of Applied Mathematics and Informatics, Hanoi University of Technology,

 No. 1, Dai Co Viet, Hanoi, Vietnam

 

Abstract. In this paper, we introduce a new polyconvolution for integral transforms in order to solve a class of integral equations and also systems of two or three equations with generalized Toeplitz plus Hankel kernel, whose solutions can be obtained in a closed form. Estimation of the new polyconvolution in weighted Lp spaces is obtained.

2000 Mathematics Subject Classification: 44A35, 44A38, 45E10.

Keywords: Fourier transform, Kontorovich-Lebedev transform, modified Bessel function, Toeplitz plus Hankel integral equations, system of integral equations, inequality, convolution

Email: tuantrinhpsac@yahoo.com  [Corresponding Author]   

 

 

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