A Wiener-Hopf Integral Equation with a Nonsymmetric Kernel in the Supercritical Case

摘要

The paper is devoted to the solvability questions of the Wiener-Hopf integral equation in the case where the kernel K satisfies the conditions 0 <= K is an element of L-1(R), integral(infinity)(-infinity) K(t) dt > 1, K(+/- x) is an element of C-(3)(R+), (-1)K-n(+/- x)((n))(x) >= 0, x is an element of R+, n = 1, 2, 3. Based on Volterra factorization of the Wiener-Hopf operator, and invoking the technique of nonlinear functional equations, we construct real-valued solutions both for homogeneous and non-homogeneous Wiener-Hopf equations, assuming that the function g is real-valued and summable, and the corresponding conditions are satisfied. The behavior at infinity of the corresponding solutions is also studied.