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Let $G = *_{j = 1}^{q + 1} G_{n_{j} + 1}$ be the product of $q + 1$ finite groups each having order $n_{j} + 1$ and let $μ$ be the probability measure which takes the value $p_{j} / n_{j}$ on each element of $G_{n_{j} + 1} ∖ {e}$ . In this paper we shall describe the point spectrum of $μ$ in $C_{reg}^{*} (G)$ and the corresponding eigenspaces. In particular we shall see that the point spectrum occurs only for suitable choices of the numbers $n_{j}$ . We also compute the continuous spectrum of $μ$ in $C_{reg}^{*} (G)$ in several cases. A family of irreducible representations of $G$ , parametrized on the continuous spectrum of $μ$ ,...

Random walks on the affine group of local fields and of homogeneous trees

Donald I. Cartwright, Vadim A. Kaimanovich, Wolfgang Woess (1994)

Annales de l'institut Fourier

The affine group of a local field acts on the tree $𝕋 (𝔉)$ (the Bruhat-Tits building of $GL (2, 𝔉)$ ) with a fixed point in the space of ends $\partial 𝕋 (F)$ . More generally, we define the affine group $Aff (𝔉)$ of any homogeneous tree $𝕋$ as the group of all automorphisms of $𝕋$ with a common fixed point in $\partial 𝕋$ , and establish main asymptotic properties of random products in $Aff (𝔉)$ : (1) law of large numbers and central limit theorem; (2) convergence to $\partial 𝕋$ and solvability of the Dirichlet problem at infinity; (3) identification of the Poisson boundary...

Random weighted Sidon sets

Kathryn Hare (2000)

Colloquium Mathematicae

We investigate random Sidon-type sets in which the degrees of the representations are weighted. These variants of Sidon sets are of interest as there are compact non-abelian groups which admit no infinite Sidon sets. In this note we determine the largest weight function such that infinite random weighted Sidon sets exist in all infinite compact groups.

Range of the horocyclic Radon transform on trees

Enrico Casadio Tarabusi, Joel M. Cohen, Flavia Colonna (2000)

Annales de l'institut Fourier

In this paper we study the Radon transform $R$ on the set $ℋ$ of horocycles of a homogeneous tree $T$ , and describe its image on various function spaces. We show that the functions of compact support on $ℋ$ that satisfy two explicit Radon conditions constitute the image under $R$ of functions of finite support on $T$ . We extend these results to spaces of functions with suitable decay on $T$ , whose image under $R$ satisfies corresponding decay conditions and contains distributions on $ℋ$ that are not defined pointwise....

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Rademacher variables in connection with complex scalars.

Radial Convolutors on Free Groups

Radial convolutors on free groups

Radon-Transformation auf nilpotenten Lie-Gruppen.

Rajchman measures on compact groups.

Random Fourier series on locally compact abelian groups

Random Walks on Amalgams.

Random walks on free products

Random walks on the affine group of local fields and of homogeneous trees

Random weighted Sidon sets

Range of the horocyclic Radon transform on trees

Rapidly decreasing functions on general semisimple groups

Rearrangement and continuity properties of $B M O (φ)$ functions on spaces of homogeneous type

Rearrangement of coefficients of Fourier series on $S U_{2}$

Recapturing semigroup compactifications of a group from those of its closed normal subgroups.

Recent developments in the theory of Walsh series.

Recent developments on the F. and M. Riesz theorem

Reciprocities on groups

Reciprocity theorems in the theory of representations of groups and algebras [Book]

Reciprocity theorems in the theory of representations of groups

Currently displaying 1 – 20 of 89