Analogues of spectral relations for Wiener-Hopf operators with Mellin convolution (Q1594315)

The author constructs systems of functions \(x_n^\pm (t)\) and polynomials \(\pi_n^\pm (t)\) which satisfy some analogue of spectral relations for Wiener-Hopf operators with Mellin convolution.The examples of such Wiener-Hopf operators are the following operators \(K=K_\mu+N\), where \[ N\varphi= \int_0^1 \sum_{j=0}^r \frac{C_jt^{r-j}\tau^j}{(t+\tau)^{r+1}} \varphi(\tau) d\tau \text{ and }K_\mu\varphi=\varphi(t)\cos \pi\mu-\frac{\sin \pi\mu}{\pi} \int_0^1 \frac{\varphi (\tau)}{\tau-t} d\tau, \quad 0<\Re\mu<1. \] In the case \(N=0\) such relations were given by \textit{G. Ya. Popov} [``Elastic stress concentration near stamps, cuts, thin inclusions, and supports'' (in Russian), Moskva (1982; Zbl 0543.73017)].