# Spherical functions and uniformly bounded representations of free groups

Studia Mathematica (1991)

- Volume: 100, Issue: 3, page 237-250
- ISSN: 0039-3223

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topPytlik, Tadeusz. "Spherical functions and uniformly bounded representations of free groups." Studia Mathematica 100.3 (1991): 237-250. <http://eudml.org/doc/215886>.

@article{Pytlik1991,

abstract = {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.},

author = {Pytlik, Tadeusz},

journal = {Studia Mathematica},

keywords = {free group; uniformly bounded representation; spherical functions; analytic series of representations; unitary representations},

language = {eng},

number = {3},

pages = {237-250},

title = {Spherical functions and uniformly bounded representations of free groups},

url = {http://eudml.org/doc/215886},

volume = {100},

year = {1991},

}

TY - JOUR

AU - Pytlik, Tadeusz

TI - Spherical functions and uniformly bounded representations of free groups

JO - Studia Mathematica

PY - 1991

VL - 100

IS - 3

SP - 237

EP - 250

AB - 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.

LA - eng

KW - free group; uniformly bounded representation; spherical functions; analytic series of representations; unitary representations

UR - http://eudml.org/doc/215886

ER -

## References

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- [10] T. Pytlik, Spherical functions and uniformly bounded representations of free groups, preprint 60 (1986), Math. Inst. Univ. Wrocław. Zbl0754.22002
- [11] T. Pytlik and R. Szwarc, An analytic family of uniformly bounded representations of free groups, Acta Math. 157 (1986), 287-309. Zbl0681.43011
- [12] S. Sawyer, Isotropic random walks in a tree, Z. Wahrsch. Verw. Gebiete 12 (1978), 279-292. Zbl0362.60075
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- [14] A. Valette, Cocycles d'arbres et représentations uniformément bornées, C. R. Acad. Sci. Paris 310 (1990), 703-708. Zbl0828.22007

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