کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6418470 | 1339335 | 2014 | 19 صفحه PDF | دانلود رایگان |
The problem of the embeddability of two commuting continuous injections f,g:I=(0,b]âI 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 {ft:IâI,tâT} of continuous injections for which fuâfv=fu+v, u,vâT, such that f=f1 and g=fs for an sâT and sâQ, where TâR+ is a dense semigroup which can be extended to a group. We determine a maximal semigroup of indices Sem(f,g)âR+ such that for every T-iteration semigroup TâSem(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.
Journal: Journal of Mathematical Analysis and Applications - Volume 416, Issue 2, 15 August 2014, Pages 862-880