Acta Mathematica Vietnamica
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ON THE CONVOLUTION WITH A WEIGHT-FUNCTION FOR THE COSINE-FOURIER INTEGRAL TRANSFORM
NGUYEN XUAN THAO, NGUYEN MINH KHOApp. 149-162
Abstract
The convolution with a weight-function for the cosine-Fourier transform is formulated and its properties are studied. A Titchmarch type theorem, non-existence of the unit element of the convolution are proved. The relationship between the convolution with and without a weight-function is estabilished and the application to solving integral equations is outlined.