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Vladikavkazskii Matematicheskii Zhurnal, 2015, Volume 17, Number 3, Pages 53–55
(Mi vmj552)
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A remark on absolutely convergent series in spaces of germs of analytic functions
S. N. Melikhovab a Southern Federal University, Rostov-on-Don, Russia
b Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia
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 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.
Key words:
space of germs of analytic functions, absolutely convergent series, convex locally closed set.
Received: 15.05.2015
Citation:
S. N. Melikhov, “A remark on absolutely convergent series in spaces of germs of analytic functions”, Vladikavkaz. Mat. Zh., 17:3 (2015), 53–55
Linking options:
https://www.mathnet.ru/eng/vmj552 https://www.mathnet.ru/eng/vmj/v17/i3/p53
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Abstract page: | 167 | Full-text PDF : | 58 | References: | 31 |
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