o-极小全纯函数的分段Weierstrass预处理与除法
Piecewise Weierstrass preparation and division for o-minimal holomorphic functions
摘要：
给出了实域上的一个o-极小结构，证明了可定义全纯函数的一个分段Weierstrass准备定理和一个分段Weierstrass除法定理.在半代数条件下，对于整体次解析集和函数的结构，我们得到了可定义实解析函数的相应结果。作为应用，我们给出了主理想的可定义的全局零点空间.
英文摘要：
Given an o-minimal structure expanding the field of reals, we show a piecewise Weierstrass preparation theorem and a piecewise Weierstrass division theorem for definable holomorphic functions. In the semialgebraic setting and for the structure of globally subanalytic sets and functions we obtain the corresponding results for definable real analytic functions. As an application we show a definable global Nullstellensatz for principal ideals.
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