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Vietnam Journal of Mathematics 36:1(2008) 83-101

Integral Transforms Related to the Fourier Sine Convolution with a Weight Function  

Nguyen Xuan Thao and Nguyen Thanh Hong

Abstract.  Integral transforms of the form

from L_p(R₊) to L_q(R₊), (1 p 2, p^-1 + q^-1 = 1) are studied. Watson's and Plancherel's Theorems are obtained. Applications to solving integral equation and systems of integral equations are considered.

2000 Mathematics Subject Classification: 44A05, 44A35.

Keywords: Integral transform, convolution, Fourier sine transform, Plancherel theorem, integral equation.

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Published by Springer since January 2013