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Piecewise Weierstrass preparation and division for o-minimal holomorphic functions


Author: Tobias Kaiser
Journal: Proc. Amer. Math. Soc. 145 (2017), 3887-3897
MSC (2010): Primary 32B05; Secondary 03C64, 32B20, 32C07
DOI: https://doi.org/10.1090/proc/13507
Published electronically: February 21, 2017
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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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Tobias Kaiser
Affiliation: Faculty of Computer Science and Mathematics, University of Passau, 94030 Passau, Germany
Email: tobias.kaiser@uni-passau.de

DOI: https://doi.org/10.1090/proc/13507
Received by editor(s): June 9, 2016
Received by editor(s) in revised form: September 19, 2016, and September 23, 2016
Published electronically: February 21, 2017
Communicated by: Franc Forstneric
Article copyright: © Copyright 2017 American Mathematical Society

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