On semibounded Wiener-Hopf operators

Abstract

We show that a semibounded Wiener-Hopf quadratic form is closable in the space $L^2({\mathbb{R}}_{+})$ 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.

References in corpus (1)

• Quasi-diagonalization of Hankel operators

Cited by in corpus (1)

• Toeplitz versus Hankel: semibounded operators