The argument principle and holomorphic extendibility to finite Riemann surfaces

Josip Globevnik

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The argument principle and holomorphic extendibility to finite Riemann surfaces

Josip Globevnik

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Abstract

Let M be a finite Riemann surface and let A(bM) be the algebra of all continuous functions on bM which extend holomorphically through M. We prove that a continuous function F on bM belongs to A(bM) if for each f, g in A(bM) such that fF+g has no zero the change of argument of fF+g along bM is nonnegative.

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Josip Globevnik. 2005-07-30. The argument principle and holomorphic extendibility to finite Riemann surfaces. https://arxiv.org/abs/math/0508012

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