The winding number of Pf+1 for polynomials P and meromorphic extendibility of f

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:393

Article

Globevnik, Josip

关键词: Meromorphic extensions;    Argument principle;   

DOI  :  10.1016/j.jmaa.2012.03.061

来源: Elsevier

【 摘 要 】

Let Delta be the open unit disc in C. The paper deals with the following conjecture: if f is a continuous function on b Delta such that the change of argument of Pf + 1 around b Delta is nonnegative for every polynomial P such that Pf + 1 has no zero on b Delta then f extends holomorphically through Delta. 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. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free