Piecewise Weierstrass preparation and division for o-minimal holomorphic functions

2016/06/08 by Kaiser, Tobias
#03C64 #32B05 #32B20 #32C07 #Complex Variables (math.CV) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1606.02591

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.

Related

• Fibers of flat morphisms and Weierstrass preparation theorem
• Definability of complex functions in o-minimal structures
• Note on the Weierstrass Preparation Theorem in Quasianalytic Local Rings
• On Preparation Theorems for ℝ_an,exp-definable functions
• Weierstrass preparation theorem and singularities in the space of\n non-degenerate arcs