Integral Transforms of Fourier Cosine and Sine Generalized Convolution Type

Nguyen Xuan Thao, Vu Kim Tuan and Nguyen Thanh Hong

International Journal of Mathematics and Mathematical Sciences, 2007, vol. 2007, 1-11

Abstract:

Integral transforms of the form f ( x ) ↦ g ( x ) = ( 1 − d 2 / d x 2 ) { ∫ 0 ∞ k 1 ( y ) [ f ( | x + y − 1 | ) + f ( | x − y + 1 | ) − f ( x + y + 1 ) − f ( | x − y − 1 | ) ] d y + ∫ 0 ∞ k 2 ( y ) [ f ( x + y ) + f ( | x − y | ) ] d y } from L p ( ℠+ ) to L q ( ℠+ ) , ( 1 ≤ p ≤ 2 , p − 1 + q − 1 = 1 ) are studied. Watson's and Plancherel's theorems are obtained.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:097250

DOI: 10.1155/2007/97250

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