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Fréchet-valued meromorphic extension along a pencil of complex lines. (English) Zbl 1493.32008

Summary: The aim of paper is to find the condition under which a Fréchet-valued function \(f\in C^\infty(\{0\})\) admitting meromorphic extension along some pencil of complex lines can be meromorphically extended to a neighborhood of \(0\in \mathbb{C}^N.\) Some auxiliary results concerning the domains of existence for Fréchet-valued meromorphic functions, Rothstein’s theorem, Levi extension theorem for meromorphic functions with values in a locally complete space, convergence of formal power series of Fréchet-valued homogeneous polynomials are also proved in this work.

MSC:

32K12 Holomorphic maps with infinite-dimensional arguments or values
32A20 Meromorphic functions of several complex variables
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