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Volume
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Vietnam
Journal of Mathematics 39:2 (2011) 217-235
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A New Polyconvolution and Its Application to
Solving
a Class of Toeplitz Plus Hankel Integral Equations
and Systems of Integral Equations
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Trinh Tuan1 and Nguyen Xuan
Thao2
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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
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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.
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2000 Mathematics Subject Classification: 44A35, 44A38,
45E10.
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Keywords: Fourier
transform, Kontorovich-Lebedev transform, modified Bessel function,
Toeplitz plus Hankel integral equations, system of integral equations,
inequality, convolution
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Email: tuantrinhpsac@yahoo.com [Corresponding Author]
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
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Published
by Springer since January 2013
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