The winding number of PF+1 for polynomials P and meromorphic extendibility of F

Details The winding number of PF+1 for polynomials P and meromorphic extendibility of F The winding number of PF+1 for polynomials P and meromorphic extendibility of F

2012-02-08

arxiv.org/abs/1202.1669v1

Mathematics

Complex Variables

13 pages

Scientific paper

Let D be the open unit disc in C. The paper deals with the following conjecture: If f is a continuous function on bD such that the change of argument of Pf+1 around bD is nonnegative for every polynomial P such that Pf+1 has no zero on bD then f extends holomorphically through D. We prove a related result on meromorphic extendibility for smooth functions with finitely many zeros of finite order, which, in particular, implies that the conjecture holds for real analytic functions.

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