On biorthogonal systems generated by some involutive operators (Q2387035)

There are studied conditions for solvability and properties of solutions to singular integral equations with a perturbed singular integral operator with fixed singularity, where \[ (S\varphi)(t)=\frac{1}{\pi i}\int_\Gamma E (\tau-t)\varphi(\tau)d\tau, \] \[ E(2)=z^{-1}+ (2+1+i)^{-1}+(2+1-i)^{-1}+(2-1+i)^{-1}+(2-1-i)^{-1}, \] \(\Gamma =\partial R\) and \(R\) is a square with vertices \(\mp \frac 12(1\pm i)\). Reviewer's remark: The name ``Sokhotskiĭ'' (in Russian: Сохоцкий) should be written in the Latin alphabet as Sochocki. Indeed, J. Sochocki (1842--1927), born in Warsaw, studied and worked in Sankt Petersburg (later: Leningrad). He took part in the Polish uprising 1863.