ON THE CONVOLUTION WITH WEIGHT-FUNCTION FOR THE FOURIER SIN INTEGRAL TRANSFORM

Abstract

The convolution with a weight-function for the Fourier sine integral

transform is formulated and its properties are studied. A Titchmarch

type theorem, non-existence of the unit element of the convolution are

proved. The application to solve some particular cases of the Toeplitz

plus Hankel integral equations is outlined.