Piecewise Weierstrass preparation and division for o-minimal holomorphic functions
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- by Tobias Kaiser PDF
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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.References
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Additional Information
- Tobias Kaiser
- Affiliation: Faculty of Computer Science and Mathematics, University of Passau, 94030 Passau, Germany
- MR Author ID: 684790
- Email: tobias.kaiser@uni-passau.de
- 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
- © Copyright 2017 American Mathematical Society
- 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
- MathSciNet review: 3665041