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arXiv math/0606727math.CV
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度与全纯扩张

Degree and holomorphic extensions

Josip Globevnik

摘要:

设D是C^N,N \geq 2中的有界凸区域.本文证明了从bD到C^N的连续映射F全纯扩张通过D的充要条件是对每个从C^N到C^N的多项式映射P,使得F +P在bD上没有零点,|bD是非负的。我们还证明了另一个这样的定理更一般的域。

英文摘要:

Let D be a bounded convex domain in C^N, N\geq 2. We prove that a continous map F from bD to C^N extends holomorphically through D if and only if for every polynomial map P from C^N to C^N such that F+P has no zero on bD, the degree of F+P|bD is nonnegative. We also prove another such theorem for more general domains.

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。

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