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Global complexification of real analytic globally subanalytic functions

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Abstract

We show that a globally subanalytic function that is real analytic can be extended in a globally subanalytic way to a holomorphic function. We also establish a parametric version of this result. For other important ominimal structures, we show that unary definable real analytic functions can be extended definably to a holomorphic function.

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Authors and Affiliations

  1. Faculty of Computer Science and Mathematics, University of Passau, 94030, Passau, Germany

    Tobias Kaiser

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  1. Tobias Kaiser
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Correspondence to Tobias Kaiser.

Additional information

The author was supported in part by DFG KA 3297/1-2.

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Kaiser, T. Global complexification of real analytic globally subanalytic functions. Isr. J. Math. 213, 139–173 (2016). https://doi.org/10.1007/s11856-016-1306-9

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  • DOI: https://doi.org/10.1007/s11856-016-1306-9

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