Spectral Representations of the Wiener-Hopf Operator for the sinc Kernel and some Related Operators

Abstract

The spectral representation of the Wiener-Hopf operator K with kernel 1 π sinc is given determining explicitly the Hilbert space isomorphism, which transforms K into the multiplication operator by the identity on L 2 (0, 1). Several related integral operators are studied. A close relationship of K to the finite Hilbert transformation is revealed yielding the spectral representation of the latter. This is of particular interest as it concerns a general feature of self-adjoint Wiener-Hopf operators [15].