Integral Transforms of Fourier Cosine and Sine Generalized Convolution Type

Thao, Nguyen Xuan; Tuan, Vu Kim; Hong, Nguyen Thanh

doi:https://doi.org/10.1155/2007/97250

International Journal of Mathematics and Mathematical Sciences

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Research Article | Open Access

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

Integral Transforms of Fourier Cosine and Sine Generalized Convolution Type

Nguyen Xuan Thao,¹Vu Kim Tuan,²and Nguyen Thanh Hong³

Academic Editor: Piotr Mikusinski

Received05 Apr 2007

Accepted27 Aug 2007

Published17 Dec 2007

Abstract

Integral transforms of the form f(x)↦g(x)=(1−d2/dx2){∫0∞k1(y)[f(|x+y−1|)+f(|x−y+1|)−f(x+y+1)−f(|x−y−1|)]dy+∫0∞k2(y)[f(x+y)+f(|x−y|)]dy} from Lp(ℝ+) to Lq(ℝ+), (1≤p≤2,p−1+q−1=1) are studied. Watson's and Plancherel's theorems are obtained.

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Copyright

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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