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Displaying similar documents to “Twisted spherical means in annular regions in ℂ n and support theorems”

A spectral Paley-Wiener theorem for the Heisenberg group and a support theorem for the twisted spherical means on ℂ n

E. K. Narayanan, S. Thangavelu (2006)

Annales de l’institut Fourier

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We prove a spectral Paley-Wiener theorem for the Heisenberg group by means of a support theorem for the twisted spherical means on ℂ n . If f ( z ) e 1 4 | z | 2 is a Schwartz class function we show that f is supported in a ball of radius B in ℂ n if and only if f × μ r ( z ) = 0 for r > B + | z | for all z ∈ ℂ n . This is an analogue of Helgason’s support theorem on Euclidean and hyperbolic spaces. When n = 1 we show that the two conditions f × μ r ( z ) = μ r × f ( z ) = 0 for r > B + | z | imply a support theorem for a large class of functions with exponential growth. Surprisingly enough,this...

Combinatorial and group-theoretic compactifications of buildings

Pierre-Emmanuel Caprace, Jean Lécureux (2011)

Annales de l’institut Fourier

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Let X be a building of arbitrary type. A compactification 𝒞 sph ( X ) of the set Res sph ( X ) of spherical residues of X is introduced. We prove that it coincides with the horofunction compactification of Res sph ( X ) endowed with a natural combinatorial distance which we call the . Points of 𝒞 sph ( X ) admit amenable stabilisers in Aut ( X ) and conversely, any amenable subgroup virtually fixes a point in 𝒞 sph ( X ) . In addition, it is shown that, provided Aut ( X ) is transitive enough, this compactification also coincides with the group-theoretic...

Spherical conjugacy classes and the Bruhat decomposition

Giovanna Carnovale (2009)

Annales de l’institut Fourier

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Let G be a connected, reductive algebraic group over an algebraically closed field of zero or good and odd characteristic. We characterize spherical conjugacy classes in G as those intersecting only Bruhat cells in G corresponding to involutions in the Weyl group of  G .

On the Fefferman-Phong inequality

Abdesslam Boulkhemair (2008)

Annales de l’institut Fourier

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We show that the number of derivatives of a non negative 2-order symbol needed to establish the classical Fefferman-Phong inequality is bounded by n 2 + 4 + ϵ improving thus the bound 2 n + 4 + ϵ obtained recently by N. Lerner and Y. Morimoto. In the case of symbols of type S 0 , 0 0 , we show that this number is bounded by n + 4 + ϵ ; more precisely, for a non negative symbol a , the Fefferman-Phong inequality holds if ∂ x α ∂ ξ β a ( x , ξ ) are bounded for, roughly, 4 ≤ | α | + | β | ≤ n + 4 + ϵ . To obtain such results and others, we first prove an abstract result which...