Application of multiple factorization to convolution-type homogeneous equations (Q1382901)

The author studies the homogeneous Wiener-Hopf plus Hankel equation \[ f(x)= \int_0^\infty K(x-t)f(t) dt +\lambda\int_0^\infty K_0(x+t)f(t) dt, \qquad t>0 \] with summable kernels \(K(t)\) and \(K_0(t)\). It is assumed that \(\lambda \in \mathbb{C}\) and \(K(t)\) is nonnegative and satisfies the conservative condition \(\mu= \int_{-\infty}^{+\infty} K(t) dt = 1\). Under some assumption he shows that the considered equation has a non-trivial continuous solution. The case \(K_0(t)=K(t)\) is also examined.