Piecewise Weierstrass preparation and division for o-minimal holomorphic functions

Kaiser, Tobias

doi:10.1090/proc/13507

Piecewise Weierstrass preparation and division for o-minimal holomorphic functions
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by Tobias Kaiser PDF

Proc. Amer. Math. Soc. 145 (2017), 3887-3897 Request permission

Abstract:

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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