Wiener-Hopf equation in supercritical case (Q1382903)

The author studies the Wiener-Hopf equation \[ \varphi (t)= f(t)+ \int_0^\infty K(t-\tau)\varphi (\tau ) d\tau, \qquad t>0 \] with nonnegative kernel \(K(t) \in L_1(R)\) satisfying the condition \(\mu= \int_{-\infty}^{+\infty} K(t) dt > 1\). Assuming that \(\int_{-\infty}^{+\infty}| t|^j K(t) dt< \infty\), \(j=1,\dots,4\) he investigates the properties of the symbol under the assumption that the norm \(\mu\) is sufficiently close to 1. The application of investigating the Wiener-Hopf equation with a degenerate symbol is given.