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We give a simple proof of a result of R. Rochberg and M. H. Taibleson that various maximal operators on a homogeneous tree, including the Hardy-Littlewood and spherical maximal operators, are of weak type (1,1). This result extends to corresponding maximal operators on a transitive group of isometries of the tree, and in particular for (nonabelian finitely generated) free groups.

Admissible distributions on p-adic symmetric spaces.

Jeffrey Hakim (1994)

Journal für die reine und angewandte Mathematik

An example of Fourier transforms of orbital integrals and their endoscopic transfer.

Everling, Ulrich (1998)

The New York Journal of Mathematics [electronic only]

An inequality for local unitary Theta correspondence

Z. Gong, L. Grenié (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

Given a representation $π$ of a local unitary group $G$ and another local unitary group $H$ , either the Theta correspondence provides a representation $θ_{H} (π)$ of $H$ or we set $θ_{H} (π) = 0$ . If $G$ is fixed and $H$ varies in a Witt tower, a natural question is: for which $H$ is $θ_{H} (π) \neq 0$ ? For given dimension $m$ there are exactly two isometry classes of unitary spaces that we denote $H_{m}^{\pm}$ . For $ε \in {0, 1}$ let us denote $m_{ε}^{\pm} (π)$ the minimal $m$ of the same parity of $ε$ such that $θ_{H_{m}^{\pm}} (π) \neq 0$ , then we prove that $m_{ε}^{+} (π) + m_{ε}^{-} (π) \geq 2 n + 2$ where $n$ is the dimension of $π$ .

Analyse harmonique des groupes d'automorphismes d'arbres de Bruhat-Tits

Francis M. Choucroun (1994)

Mémoires de la Société Mathématique de France

Arithmetic aspect of operator algebras

R. J. Plymen, C. W. Leung (1991)

Compositio Mathematica

Asymptotic behaviour of supercuspidal characters of $p$ -adic ${𝐆𝐒𝐩}_{(4)}$

Fiona Murnaghan (1991)

Compositio Mathematica

Base change for Bernstein centers of depth zero principal series blocks

Thomas J. Haines (2012)

Annales scientifiques de l'École Normale Supérieure

Let $G$ be an unramified group over a $p$ -adic field. This article introduces a base change homomorphism for Bernstein centers of depth-zero principal series blocks for $G$ and proves the corresponding base change fundamental lemma. This result is used in the approach to Shimura varieties with $Γ_{1} (p)$ -level structure initiated by M. Rapoport and the author in [15].

Bornes inférieures pour les marches aléatoires sur les groupes p-adiques moyennables

Sami Mustapha (2006)

Annales de l'I.H.P. Probabilités et statistiques

Characters of supercuspidal representations of classical groups

Fiona Murnaghan (1996)

Annales scientifiques de l'École Normale Supérieure

Degenerate principal series for orthogonal groups.

Chris Jantzen (1993)

Journal für die reine und angewandte Mathematik

Dual Blobs and Plancherel Formulas

Ju-Lee Kim (2004)

Bulletin de la Société Mathématique de France

Let $k$ be a $p$ -adic field. Let $G$ be the group of $k$ -rational points of a connected reductive group $𝖦$ defined over $k$ , and let $𝔤$ be its Lie algebra. Under certain hypotheses on $𝖦$ and $k$ , wequantifythe tempered dual $\hat{G}$ of $G$ via the Plancherel formula on $𝔤$ , using some character expansions. This involves matching spectral decomposition factors of the Plancherel formulas on $𝔤$ and $G$ . As a consequence, we prove that any tempered representation contains a good minimal $𝖪$ -type; we extend this result to irreducible...

Endoscopie et changement de caractéristique : intégrales orbitales pondérées

Jean-Loup Waldspurger (2009)

Annales de l’institut Fourier

La stabilisation de la formule des traces utilise non seulement le “lemme fondamental”, mais aussi plusieurs variantes dont l’une est le “lemme fondamental pondéré”. Nous montrons que, si celui-ci est vrai sur un corps de base de caractéristique positive, il l’est aussi sur un corps de base de caractéristique nulle. Pour cela, nous introduisons un certain espace de fonctions contenant les fonctions caractéristiques des réseaux de Moy-Prasad. Nous montrons que les intégrales orbitales pondérées des...

Erratum à l’article : «Représentations modulaires de $G L (2, F)$ en caractéristique $l$ , $F$ corps $p$ -adique, $p \neq l$ »

Marie-France Vignéras (1996)

Compositio Mathematica

Euler characteristics for $p$ -adic Lie groups

Burt Totaro (1999)

Publications Mathématiques de l'IHÉS

Explicit Kazhdan constants for representations of semisimple and arithmetic groups

Yehuda Shalom (2000)

Annales de l'institut Fourier

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 explicitly....

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