Displaying similar documents to “Injectivity Sets for Spherical Means on the Heisenberg Group.”

Asymptotic spherical analysis on the Heisenberg group

Jacques Faraut (2010)

Colloquium Mathematicae

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The asymptotics of spherical functions for large dimensions are related to spherical functions for Olshanski spherical pairs. In this paper we consider inductive limits of Gelfand pairs associated to the Heisenberg group. The group K = U(n) × U(p) acts multiplicity free on 𝓟(V), the space of polynomials on V = M(n,p;ℂ), the space of n × p complex matrices. The group K acts also on the Heisenberg group H = V × ℝ. By a result of Carcano, the pair (G,K) with G = K ⋉ H is a Gelfand pair....

Spherical quadrangles.

Avelino, Catarina P., Breda, A.M.d'Azevedo, Santos, Altino F. (2010)

Beiträge zur Algebra und Geometrie

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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.

On the five-point theorems due to Lappan

Yan Xu (2011)

Annales Polonici Mathematici

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By using an extension of the spherical derivative introduced by Lappan, we obtain some results on normal functions and normal families, which extend Lappan's five-point theorems and Marty's criterion, and improve some previous results due to Li and Xie, and the author. Also, another proof of Lappan's theorem is given.