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Mat. Zametki, 2017, Volume 102, Issue 3, Pages 396–404 (Mi mz11329)  

This article is cited in 2 scientific papers (total in 2 papers)

Embedding of a Uniquely Divisible Abelian Semigroup In a Convex Cone

I. V. Orlov

Crimea Federal University, Simferopol

Abstract: It is proved that every uniquely divisible Abelian semigroup admits an injective subadditive embedding in a convex cone. As an application, the classical theory of generators of one-parameter operator semigroups is generalized to the case in which the parameter ranges over a uniquely divisible semigroup.

Keywords: Abelian semigroup, unique divisibility, convex cone, infinitesimal generator of an operator semigroup.

DOI: https://doi.org/10.4213/mzm11329

Full text: PDF file (485 kB)
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English version:
Mathematical Notes, 2017, 102:3, 361–368

Bibliographic databases:

Document Type: Article
UDC: 512.53+517.98
Received: 29.07.2016
Revised: 15.03.2017

Citation: I. V. Orlov, “Embedding of a Uniquely Divisible Abelian Semigroup In a Convex Cone”, Mat. Zametki, 102:3 (2017), 396–404; Math. Notes, 102:3 (2017), 361–368

Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm11329
  • http://mi.mathnet.ru/eng/mz/v102/i3/p396

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. V. Orlov, “Generalized Hamel basis and basis extension in convex cones and uniquely divisible semigroups”, Eurasian Math. J., 9:1 (2018), 69–82  mathnet
    2. F. S. Stonyakin, “On Sublinear Analogs of Weak Topologies in Normed Cones”, Math. Notes, 103:5 (2018), 859–864  mathnet  crossref  crossref  isi  elib
  • Математические заметки Mathematical Notes
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