On semibounded Wiener–Hopf operators

We show that a semibounded Wiener–Hopf quadratic form is closable in the space L2(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.