Finiteness of the discrete spectrum of the perturbed Wiener-Hopf operator (Q578561)

Consider the Wiener-Hopf operator A on \(L^ 2(R_+)\) defined by \[ Af(x)=\int^{\infty}_{0}k(x-y)f(y)dy,\quad x>0,\quad k(x)\in L^ 1(R), \] and assume that for some \(\tau >0\) the kernel k(x) satisfies \(e^{\tau | x|}k(x)\in L^ 1(R)\). Let T be an integral operator on \(L^ 2(R_+)\). The author puts certain conditions on the kernel of T and concludes that the discrete spectrum of the perturbed operator \(A+T\) is finite.