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A remark on absolutely convergent series in spaces of germs of analytic functions. (Russian. English summary) Zbl 1474.32031

Summary: It is proved that each absolutely convergent series in the space of germs of all analytic functions on a some set \(M\subset\mathbb C^N\) endowed with the projective topology converges absolutely in the Fréchet space of analytic functions on an open neighborhood of \(M\). In particular, this allows us to remove the assumptions about the growth of exponents of exponential series, posed in some previous statements.

MSC:

32B10 Germs of analytic sets, local parametrization
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References:

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