On one-parameter semigroups generated by commuting continuous injections

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:416

Article

Krassowska, Dorota¹  Zdun, Marek Cezary¹ 

[1] Pedag Univ, Inst Math, Krakow, Poland

关键词: Iteration semigroup;    Semi-flows;    Iterates;    Abel's functional equation;    Set valued-functions;    Cantor;   

DOI  :  10.1016/j.jmaa.2014.03.021

来源: Elsevier

【 摘 要 】

The problem of the embeddability of two commuting continuous injections f, g : I = (0, b] I in Abelian semigroups is discussed. We consider the case when there is no iteration semigroup in which f and g can be embedded. Explaining this phenomenon we modify the definition of an iteration semigroup introducing a new notion - a T-iteration semigroup of f and g, that is a family {f(t) : I -> I , t is an element of T} of continuous injections for which f(u) o f(v) = f(u+v), u, v is an element of T, such that f = f(1) and g = f(s) for an s is an element of T and s is not an element of Q, where T subset of R+ is a dense semigroup which can be extended to a group. We determine a maximal semigroup of indices Sem(f, g) subset of R+ such that for every T-iteration semigroup T subset of Sem(f, g). We give also a construction of maximal T-iteration semigroups of f and g that is such semigroups for which T = Sem(f, g). We examine also some other Abelian semigroups of continuous functions containing f and g. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free