A central limit theorem on the space of positive definite symmetric matrices

Piotr Graczyk

Displaying similar documents to “A central limit theorem on the space of positive definite symmetric matrices”

The asymptotics of spherical functions and the central limit theorem on symmetric cones

Genkai Zhang (1995)

Annales de l'institut Fourier

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We prove a central limit theorem for certain invariant random variables on the symmetric cone in a formally real Jordan algebra. This extends form the previous results of Richards and Terras on the cone of real positive definite $n \times n$ matrices.

Bochner and Schoenberg theorems on symmetric spaces in the complex case

Piotr Graczyk, Jean-Jacques Lœb (1994)

Bulletin de la Société Mathématique de France

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Invariant analysis and contractions of symmetric spaces : part II

François Rouvière (1991)

Compositio Mathematica

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The domain of the Ornstein-Uhlenbeck operator on an $L^{p}$ -space with invariant measure

Giorgio Metafune, Jan Prüss, Abdelaziz Rhandi, Roland Schnaubelt (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We show that the domain of the Ornstein-Uhlenbeck operator on $L^{p}$ $(ℝ^{N}, μ d x)$ equals the weighted Sobolev space $W^{2, p} (ℝ^{N}, μ d x)$ , where $μ d x$ is the corresponding invariant measure. Our approach relies on the operator sum method, namely the commutative and the non commutative Dore-Venni theorems.

Spectra for Gelfand pairs associated with the Heisenberg group

Chal Benson, Joe Jenkins, Gail Ratcliff, Tefera Worku (1996)

Colloquium Mathematicae

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Let K be a closed Lie subgroup of the unitary group U(n) acting by automorphisms on the (2n+1)-dimensional Heisenberg group $H_{n}$ . We say that $(K, H_{n})$ is a Gelfand pair when the set $L_{K}^{1} (H_{n})$ of integrable K-invariant functions on $H_{n}$ is an abelian convolution algebra. In this case, the Gelfand space (or spectrum) for $L_{K}^{1} (H_{n})$ can be identified with the set $Δ (K, H_{n})$ of bounded K-spherical functions on $H_{n}$ . In this paper, we study the natural topology on $Δ (K, H_{n})$ given by uniform convergence on compact subsets in $H_{n}$ . We show that...

Spherical means on the Heisenberg group and a restriction theorem for the symplectic Fourier transform.

Sundaram Thangavelu (1991)

Revista Matemática Iberoamericana

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The aim of this paper is to study mean value operators on the reduced Heisenberg group H/Γ, where H is the Heisenberg group and Γ is the subgroup {(0,2πk): k ∈ Z} of H.

Spherical functions on ordered symmetric spaces

Jacques Faraut, Joachim Hilgert, Gestur Ólafsson (1994)

Annales de l'institut Fourier

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We define on an ordered semi simple symmetric space $ℳ = G / H$ a family of spherical functions by an integral formula similar to the Harish-Chandra integral formula for spherical functions on a Riemannian symmetric space of non compact type. Associated with these spherical functions we define a spherical Laplace transform. This transform carries the composition product of invariant causal kernels onto the ordinary product. We invert this transform when $G$ is a complex group, $H$ a real form of $G$ ,...

Displaying similar documents to “A central limit theorem on the space of positive definite symmetric matrices”

The asymptotics of spherical functions and the central limit theorem on symmetric cones

Bochner and Schoenberg theorems on symmetric spaces in the complex case

Invariant analysis and contractions of symmetric spaces : part II

The domain of the Ornstein-Uhlenbeck operator on an L p -space with invariant measure

Spectra for Gelfand pairs associated with the Heisenberg group

Spherical means on the Heisenberg group and a restriction theorem for the symplectic Fourier transform.

Spherical functions on ordered symmetric spaces

The domain of the Ornstein-Uhlenbeck operator on an $L^{p}$ -space with invariant measure