Plemelj–Sokhotski isomorphism for quasicircles in Riemann surfaces and the Schiffer operators
Plemelj–Sokhotski isomorphism for quasicircles in Riemann surfaces and the Schiffer operators
Abstract Let R be a compact Riemann surface and $$\Gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Γ</mml:mi> </mml:math> be a Jordan curve separating R into connected components $$\Sigma _1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Σ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> and $$\Sigma _2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Σ</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> . We consider Calderón–Zygmund type operators $$T(\Sigma …