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Compact noncontraction semigroups of affine operators

Journal Article · · Sbornik. Mathematics
;  [1]
  1. M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
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.
OSTI ID:
22590453
Journal Information:
Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 7 Vol. 206; ISSN 1064-5616
Country of Publication:
United States
Language:
English

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