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Sbornik: Mathematics, 2015, Volume 206, Issue 7, Pages 921–940
DOI: https://doi.org/10.1070/SM2015v206n07ABEH004483 (Mi sm8408) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Compact noncontraction semigroups of affine operators

A. S. Voynov, V. Yu. Protasov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (561 kB) Citations (8)
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DOI: https://doi.org/10.1070/SM2015v206n07ABEH004483
Abstract: We analyze compact multiplicative semigroups of affine operators acting in a finite-dimensional space. The main result states that every such semigroup is either contracting, that is, contains elements of arbitrarily small operator norm, or all its operators share a common invariant affine subspace on which this semigroup is contracting. The proof uses functional difference equations with contraction of the argument. We look at applications to self-affine partitions of convex sets, the investigation of finite affine semigroups and the proof of a criterion of primitivity for nonnegative matrix families.
Bibliography: 32 titles.
Keywords: affine operator, self-similarity, partition, spectral radius, primitive matrix.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00332
13-01-00642
Dynasty Foundation
Simons Foundation
Ministry of Education and Science of the Russian Federation НШ-3682.2014.1
The work of the first author was supported by the Russian Foundation for Basic Research (grant no. 14-01-00332), the "Dynasty" Foundation, a Simons-IUM Fellowship, and by the Council of the President of the Russian Federation for the Support of Leading Scientific Schools (grant no. НШ-3682.2014.1); the work of the second author was supported by the Russian Foundation for Basic Research (grant nos. 13-01-00642 and 14-01-00332) and the "Dynasty" Foundation.
Received: 21.07.2014 and 11.02.2015
Russian version:
Matematicheskii Sbornik, 2015, Volume 206, Number 7, Pages 33–54
DOI: https://doi.org/10.4213/sm8408
Bibliographic databases:
Document Type: Article
UDC: 517.98+514.172.4+514.174.5
MSC: 52B45, 52C07
Language: English
Original paper language: Russian
Citation: A. S. Voynov, V. Yu. Protasov, “Compact noncontraction semigroups of affine operators”, Mat. Sb., 206:7 (2015), 33–54; Sb. Math., 206:7 (2015), 921–940
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:77
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