Browsing by Author "Gwoździewicz, Janusz"

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    Criteria for Algebraicity of Analytic Functions
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2018) Bochnak, Jacek; Gwoździewicz, Janusz; Kucharz, Wojciech
    We consider functions defined on an open subset of a nonsingular, either real or complex, algebraic set. We give criteria for an analytic function to be a Nash (resp. regular, resp. polynomial) function. Our criteria depend only on the behavior of such a function along irreducible nonsingular algebraic curves passing trough a given point. In the proofs we use results on algebraicity of formal power series, which are also established in this paper.