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DOI: 10.23671/VNC.2017.3.7264

A Remark on Absolutely Convergent Series in Spaces of Germs of Analytic Functions

Melikhov S. N.
Vladikavkaz Mathematical Journal 2015. Vol. 17. Issue 3.
Abstract:
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 Frechet 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.
Keywords: space of germs of analytic functions, absolutely convergent series, convex locally closed set
Language: Russian Download the full text  
For citation: †Melikhov S. N. A Remark on Absolutely Convergent Series in Spaces of Germs of Analytic Functions. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol.17, no. 3, pp.53-55. DOI 10.23671/VNC.2017.3.7264
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