An application of shift operators to ordered symmetric spaces

Nils Byrial Andersen; Jérémie M. Unterberger

Displaying similar documents to “An application of shift operators to ordered symmetric spaces”

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 $G$ ,...

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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Harmonic analysis on $S U (n, n) / S L (n, ℂ) \times ℝ_{+}$ .

Andersen, Nils Byrial, Unterberger, Jérémie M. (2000)

Journal of Lie Theory

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A spherical transform on Schwartz functions on the Heisenberg group associated to the action of U(p,q)

T. Godoy, L. Saal (2006)

Colloquium Mathematicae

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Let 𝓢(Hₙ) be the space of Schwartz functions on the Heisenberg group Hₙ. We define a spherical transform on 𝓢(Hₙ) associated to the action (by automorphisms) of U(p,q) on Hₙ, p + q = n. We determine its kernel and image and obtain an inversion formula analogous to the Godement-Plancherel formula.

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 harmonics and spherical averages of Fourier transforms

Per Sjölin (2002)

Rendiconti del Seminario Matematico della Università di Padova

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Fourier transform of Schwartz functions on the Heisenberg group

Francesca Astengo, Bianca Di Blasio, Fulvio Ricci (2013)

Studia Mathematica

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Let H₁ be the 3-dimensional Heisenberg group. We prove that a modified version of the spherical transform is an isomorphism between the space 𝓢ₘ(H₁) of Schwartz functions of type m and the space 𝓢(Σₘ) consisting of restrictions of Schwartz functions on ℝ² to a subset Σₘ of the Heisenberg fan with |m| of the half-lines removed. This result is then applied to study the case of general Schwartz functions on H₁.

Spherical functions and spectral synthesis

Christopher Meaney (1985)

Compositio Mathematica

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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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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...