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1
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Spherical functions and uniformly bounded representations of free groups

100%
Pytlik T.
Studia Mathematica
|
1991
|
tom 100
|
nr 3
237-250
EN
We give a construction of an analytic series of uniformly bounded representations of a free group G, through the action of G on its Poisson boundary. These representations are irreducible and give as their coefficients all the spherical functions on G which tend to zero at infinity. The principal and the complementary series of unitary representations are included. We also prove that this construction and the other known constructions lead to equivalent representations.
2
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Free operators with operator coefficients

100%
Lehner F.
Colloquium Mathematicum
|
1997
|
tom 74
|
nr 2
321-328
3
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The ratio and generating function of cogrowth coefficients of finitely generated groups

100%
Szwarc R.
Studia Mathematica
|
1998
|
tom 131
|
nr 1
89-94
EN
Let G be a group generated by r elements $g_1,…,g_r$. Among the reduced words in $g_1,…,g_r$ of length n some, say $γ_n$, represent the identity element of the group G. It has been shown in a combinatorial way that the 2nth root of $γ_{2n}$ has a limit, called the cogrowth exponent with respect to the generators $g_1,…,g_r$. We show by analytic methods that the numbers $γ_n$ vary regularly, i.e. the ratio $γ_{2n+2}/γ_{2n}$ is also convergent. Moreover, we derive new precise information on the domain of holomorphy of γ(z), the generating function associated with the coefficients $γ_n$.
4
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Representations of a free group of rank two by time-varying Mealy automata

88%
Woryna A.
Discussiones Mathematicae - General Algebra and Applications
|
2005
|
tom 25
|
nr 1
119-134
EN
In the group theory various representations of free groups are used. A representation of a free group of rank two by the so-calledtime-varying Mealy automata over the changing alphabet is given. Two different constructions of such automata are presented.
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