On the spectra of some integral operators related to the potential theory in the plane

摘要

We study point spectra of the two integral operators that are generated by the boundary values of the simple-layer potential and of the integral tightly related to the double-layer potential; the operators act on the H?lder space H~μ(C), μ∈(0,1), and on the Lebesgue space L _p(C), p>2, where Γ is a closed Lyapunov curve.