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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⊂CN 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: | 185 | Full-text PDF : | 65 | References: | 42 |
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