Solvability of a class of Wiener-Hopf integral equations (Q1362400)

The author studies the solvability problem for Wiener-Hopf equation with symbol \[ A(\lambda)=\Biggl({\lambda\over\lambda+ i}\Biggr)^jB(\lambda), \] where \(A(\lambda)\), \(B(\lambda)\in{\mathcal F}\), the algebra of functions of the form \(A(\lambda)= c+\int^\infty_{-\infty}k(t)e^{i\lambda t}dt\), \(k(t)\in L_1(R^1)\), and \(j\) is some natural number. He establishes the connection between the first- and second-order moments of the kernel \(k(t)\) and properties of the symbol and gives a formula for the general solution of the renewal equation in \(E^+= L_p\), \(1\leq p<\infty\), \(M= L_\infty\), \(C\), \(C_0\).