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

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system's guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	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 + References 1. Makarov B. M. Ob induktivnyh predelah normirovannyh prostranstv. Vestnik LGU, 1965, no. 13, vol. 3, pp. 50-58 (Russian). 2. Melihov S. N., Momm Z. On the property of the inward continuability of representing systems of exponentials on convex locally closed sets. Vladikavkaz. Mat. Zh. [Vladikavkaz. Math. J.], 2008, vol. 10, no. 2, pp. 36-45 (Russian). 3. Bonet J., Meise R., Melikhov S. N. The dual of the space of holomorphic functions on locally closed convex sets. Publ. Mat., 2005, vol. 49, pp. 487-509. 4. Martineau A. Sur la topologie des espaces de fonctions holomorphes. Math. Annal., 1966, vol. 163, pp. 62-88. The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue


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