Bochner and Schoenberg theorems on symmetric spaces in the complex case

Piotr Graczyk; Jean-Jacques Lœb

Displaying similar documents to “Bochner and Schoenberg theorems on symmetric spaces in the complex case”

Spherical harmonics and spherical averages of Fourier transforms

Per Sjölin (2002)

Rendiconti del Seminario Matematico della Università di Padova

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An application of shift operators to ordered symmetric spaces

Nils Byrial Andersen, Jérémie M. Unterberger (2002)

Annales de l’institut Fourier

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We study the action of elementary shift operators on spherical functions on ordered symmetric spaces $ℳ_{m, n}$ of Cayley type, where $m \in ℕ$ denotes the multiplicity of the short roots and $n \in ℕ$ the rank of the symmetric space. For $m$ even we apply this to prove a Paley-Wiener theorem for the spherical Laplace transform defined on $ℳ_{m, n}$ by a reduction to the rank 1 case. Finally we generalize our notions and results to $B C_{n}$ type root systems.

The Helgason-Fourier transform for symmetric spaces. II.

Mohanty, Parasar, Ray, Swagato K., Sarkar, Rudra P., Sitaram, Alladi (2004)

Journal of Lie Theory

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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 $G$ ,...

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 $𝒫_{n}$ .

On the Fourier transform on the infinite symmetric group.

Vershik, A.M., Tsilevich, N.V. (2005)

Zapiski Nauchnykh Seminarov POMI

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Some remarks on restriction of the Fourier tranform for general measures.

Per Sjölin, Fernando Soria (1999)

Publicacions Matemàtiques

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In this paper we establish a formal connection between the average decay of the Fourier transform of functions with respect to a given measure and the of that measure. We also present a generalization of the classical restriction theorem of Stein and Tomas replacing the sphere with sets of prefixed Hausdorff dimension n - 1 + α, with 0 < α < 1.