Kernels of wiener-hopf plus hankel operators with matching generating functions

Abstract

Considered are Wiener-Hopf plus Hankel operators W(a)+H(b): Lp(R+) → Lp(R+) with generating functions a and b from a subalgebra of L∞(R) containing almost periodic functions and Fourier images of L1(R)- functions. If the generating functions a and b satisfy the matching condition a(t)a(-t) = b(t)b(-t), t∈ R, an explicit description for the kernels and cokernels of the operators mentioned is given.