On the spectrum of the sum of generators of a finitely generated group, II

Pierre de la Harpe; A. Robertson; Alain Valette

Displaying similar documents to “On the spectrum of the sum of generators of a finitely generated group, II”

Explicit Kazhdan constants for representations of semisimple and arithmetic groups

Yehuda Shalom (2000)

Annales de l'institut Fourier

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Consider a simple non-compact algebraic group, over any locally compact non-discrete field, which has Kazhdan’s property $(T)$ . For any such group, $G$ , we present a Kazhdan set of two elements, and compute its best Kazhdan constant. Then, settling a question raised by Serre and by de la Harpe and Valette, explicit Kazhdan constants for every lattice $Γ$ in $G$ are obtained, for a “geometric” generating set of the form $Γ \cap B_{r}$ , where $B_{r} \subset G$ is a ball of radius $r$ , and the dependence of $r$ on $Γ$ is described...

Green functions and spectra on free products of cyclic groups

K. Aomoto, Y. Kato (1988)

Annales de l'institut Fourier

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Green functions of a stochastic operator on a free product of cyclic groups are explicitly evaluated as algebraic functions. The spectra are investigated by Morse theoretic argument.

An analytic series of irreducible representations of the free group

Ryszard Szwarc (1988)

Annales de l'institut Fourier

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Let $F_{k}$ be a free group on $k$ generators. We construct the series of uniformly bounded representations $\prod_{z}$ of $F_{k}$ acting on the common Hilbert space, depending analytically on the complex parameter z, $1 / (2 k - 1) < | z | < 1$ , such that each representation $\prod_{z}$ is irreducible. If $z$ is real or $| z | = 1 / (\sqrt{2 k - 1})$ then $\prod_{z}$ is unitary; in other cases $\prod_{z}$ cannot be made unitary. For $z \neq z^{'}$ representations $\prod_{z}$ and $\prod_{z^{'}}$ are congruent modulo compact operators.

In search of the invisible spectrum

Nikolai Nikolski (1999)

Annales de l'institut Fourier

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In this paper, we begin the study of the phenomenon of the “invisible spectrum” for commutative Banach algebras. Function algebras, formal power series and operator algebras will be considered. A quantitative treatment of the famous Wiener-Pitt-Sreider phenomenon for measure algebras on locally compact abelian (LCA) groups is given. Also, our approach includes efficient sharp estimates for resolvents and solutions of higher Bezout equations in terms of their spectral bounds. The smallest...

On the joint spectral radii of commuting Banach algebra elements

Andrzej Sołtysiak (1993)

Studia Mathematica

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Some inequalities are proved between the geometric joint spectral radius (cf. [3]) and the joint spectral radius as defined in [7] of finite commuting families of Banach algebra elements.

Spherical functions and uniformly bounded representations of free groups

Tadeusz Pytlik (1991)

Studia Mathematica

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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.

Geometry of KDV (1): Addition and the unimodular spectral classes.

Henry P. McKean (1986)

Revista Matemática Iberoamericana

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This is the first of three papers on the geometry of KDV. It presents what purports to be a foliation of an extensive function space into which all known invariant manifolds of KDV fit naturally as special leaves. The two main themes are addition (each leaf has its private one) and unimodal spectral classes (each leaf has a spectral interpretation).

The support of the associated measure to the Cowen's tridiagonal matrix.

Dolores Barrios, Venancio Tomeo, Emilio Torrano (1994)

Extracta Mathematicae

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In this paper we consider a class of three-term recurrence relations, whose associated tridiagonal matrices are subnormal operators. In this cases, there are measures associated to the polynomials given by such relations. We study the support of these measures.