Invariant analysis and contractions of symmetric spaces. Part I

François Rouvière

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Invariant analysis and contractions of symmetric spaces : part II

François Rouvière (1991)

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Convexity for invariant differential operators on semisimple symmetric spaces

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An invariant symmetric non-selfadjoint differential operator.

Thomas, Erik G.F. (2002)

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Hypoelliptic and Gevrey hypoelliptic invariant differential operators on certain symmetric spaces

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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 $G$ ,...

Invariant eigendistributions on a semisimple Lie algebra

Harish-Chandra (1965)

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

Piotr Graczyk (1992)

Annales de l'institut Fourier

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A central limit theorem is proved on the space $𝒫_{n}$ of positive definite symmetric matrices. To do this, some natural analogs of the mean and dispersion on $𝒫_{n}$ are defined and investigated. One uses a Taylor expansion of the spherical functions on $𝒫_{n}$ .