We show that a semibounded Wiener-Hopf quadratic form is closable in the space $L^2({ \Bbb R}_{ +})$ if and only if its integral kernel is the Fourier transform of an absolutely continuous measure. This allows us to define semibounded Wiener-Hopf operators and their symbols under minimal assumptions on their integral kernels. Our proof relies on a continuous analogue of the Riesz Brothers theorem obtained in the paper.
Categories: math.FA math.CA math.SP