INTEGRAL TRANSFORMS RELATED TO THE FOURIER COSINE CONVOLUTION WITH A WEIGHT FUNCTION
NGUYEN THANH HONG, NGUYEN MINH KHOA
Abstract
We study a new class of integral transforms from to , , , related to the Fourier cosine convolution with a weight function. We obtain necessary and sufficient conditions under which the new transforms are unitary in . A Plancherel type theorem and the boundedness of these integral operators are obtained. We also give several examples of the new transforms kernels.