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	Dear authors! Submission of all materials is carried out only electronically through Online Submission System in personal account. 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. ← Contents of issue


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