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

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 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 ,...