Compact noncontraction semigroups of affine operators
Journal Article
·
· Sbornik. Mathematics
- 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
Similar Records
Cox rings, semigroups and automorphisms of affine algebraic varieties
On the existence of maximal semidefinite invariant subspaces for J-dissipative operators
Automorphisms of semigroups of invertible matrices with nonnegative integer elements
Journal Article
·
Sat Feb 27 23:00:00 EST 2010
· Sbornik. Mathematics
·
OSTI ID:21301180
On the existence of maximal semidefinite invariant subspaces for J-dissipative operators
Journal Article
·
Mon Feb 27 23:00:00 EST 2012
· Sbornik. Mathematics
·
OSTI ID:21612785
Automorphisms of semigroups of invertible matrices with nonnegative integer elements
Journal Article
·
Sun Sep 30 00:00:00 EDT 2012
· Sbornik. Mathematics
·
OSTI ID:22094060