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Formule de Gutzmer pour la complexification d'une espace Riemannien symétrique

Jacques Faraut (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A Gutzmer formula for the complexification of a Riemann symmetric space. We consider a complex manifold Ω and a real Lie group G of holomorphic automorphisms of Ω . The question we study is, for a holomorphic function f on Ω , to evaluate the integral of f 2 over a G -orbit by using the harmonic analysis of G . When Ω is an annulus in the complex plane and G the rotation group, it is solved by a classical formula which is sometimes called Gutzmer’s formula. We establish a generalization of it when Ω is...

Fourier analysis, Schur multipliers on S p and non-commutative Λ(p)-sets

Asma Harcharras (1999)

Studia Mathematica

This work deals with various questions concerning Fourier multipliers on L p , Schur multipliers on the Schatten class S p as well as their completely bounded versions when L p and S p are viewed as operator spaces. For this purpose we use subsets of ℤ enjoying the non-commutative Λ(p)-property which is a new analytic property much stronger than the classical Λ(p)-property. We start by studying the notion of non-commutative Λ(p)-sets in the general case of an arbitrary discrete group before turning to the...

Fourier transform of Schwartz functions on the Heisenberg group

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

Studia Mathematica

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.

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