On meromorphic extendibility

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:351

Article

Globevnik, Josip

关键词: Meromorphic extensions;    Argument principle;   

DOI  :  10.1016/j.jmaa.2008.10.004

来源: Elsevier

【 摘 要 】

Let D be a bounded domain in the complex plane whose boundary consists of finitely many pairwise disjoint real-analytic simple closed curves. Let integral be an integrable function on bD. In the paper we show how to compute the candidates for poles of a meromorphic extension of integral through D and thus reduce the question of meromorphic extendibility to the question of holomorphic extendibility. Let A(D) be the algebra of all continuous functions on (D) over bar which are holomorphic on D. We prove that a continuous function integral on bD extends meromorphically through D if and only if there is an N is an element of N boolean OR {0} such that the change of argument of P integral + Q along bD is bounded below by -27 pi N for all P, Q is an element of A(D) such that P integral + Q not equal 0 on bD. if this is the case then the meromorphic extension of has at most N poles in D, Counting Multiplicity. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free