International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2007 / Article

Research Article | Open Access

Volume 2007 |Article ID 097250 | https://doi.org/10.1155/2007/97250

Nguyen Xuan Thao, Vu Kim Tuan, Nguyen Thanh Hong, "Integral Transforms of Fourier Cosine and Sine Generalized Convolution Type", International Journal of Mathematics and Mathematical Sciences, vol. 2007, Article ID 097250, 11 pages, 2007. https://doi.org/10.1155/2007/97250

Integral Transforms of Fourier Cosine and Sine Generalized Convolution Type

Academic Editor: Piotr Mikusinski
Received05 Apr 2007
Accepted27 Aug 2007
Published17 Dec 2007

Abstract

Integral transforms of the form f(x)g(x)=(1d2/dx2){0k1(y)[f(|x+y1|)+f(|xy+1|)f(x+y+1)f(|xy1|)]dy+0k2(y)[f(x+y)+f(|xy|)]dy} from Lp(+) to Lq(+), (1p2,p1+q1=1) are studied. Watson's and Plancherel's theorems are obtained.

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Copyright © 2007 Nguyen Xuan Thao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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