International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 97250, 11 pages
doi:10.1155/2007/97250
Integral transforms of Fourier cosine and sine generalized convolution type
Nguyen Xuan Thao1
, Vu Kim Tuan2
and Nguyen Thanh Hong3
1Hanoi Water Resources University, 175 Tay Son, Dong Da, Hanoi, Vietnam
2Department of Mathematics, University of West Georgia, Carrollton, GA30118, USA
3Haiphong University, 171 Phan Dang Luu, Kien An, Haiphong, Vietnam
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.