Singular integral equations along an open arc with solutions having singularities of higher order (Q2386833)

This paper deals with the singular integral equation \[ A(t) \varphi (t) +\frac 1{\pi i}\int_L\frac{ K(t,\tau) \varphi (\tau) }{\tau-t}\,d\tau =f(t) ,\quad t\in L-\{ c_1,\dots,c_n\}, \] where \(L\) is an open arc and \(f(t) =\widetilde{f}(t) /\prod_{k=1}^n(t-c_k)^{\lambda _k},\;\widetilde{f}(t) \in H^{\lambda-1}(L-\{ a,b\}) \). The author proves the generalized Noether theorem and solves the characteristic equation.