多项式P的PF +1的卷绕数与F的亚纯可扩性
The winding number of PF+1 for polynomials P and meromorphic extendibility of F
摘要：
设D是C中的开单位圆盘。本文讨论了如下猜想：如果f是bD上的连续函数，使得Pf+1的辐角在bD周围的变化对每个多项式P都是非负的，使得Pf+1在bD上没有零点，则f全纯地扩张通过D.本文证明了关于有穷级具有多个零点的光滑函数的亚纯可扩性的一个相关结果，特别地，它暗示了该猜想对实解析函数也成立.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
