The argument principle and holomorphic extendibility to finite Riemann surfaces

Details The argument principle and holomorphic extendibility to finite Riemann surfaces The argument principle and holomorphic extendibility to finite Riemann surfaces

2005-07-30

arxiv.org/abs/math/0508012v1

Mathematics

Complex Variables

7 pages, to appear in Math.Z

Scientific paper

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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