Displaying similar documents to “Gelfand transforms of S O ( 3 ) -invariant Schwartz functions on the free group N 3 , 2 ”

A nilpotent Lie algebra and eigenvalue estimates

Jacek Dziubański, Andrzej Hulanicki, Joe Jenkins (1995)

Colloquium Mathematicae

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The aim of this paper is to demonstrate how a fairly simple nilpotent Lie algebra can be used as a tool to study differential operators on ℝ n with polynomial coefficients, especially when the property studied depends only on the degree of the polynomials involved and/or the number of variables.

Simultaneous reduction to normal forms of commuting singular vector fields with linear parts having Jordan blocks

Masafumi Yoshino, Todor Gramchev (2008)

Annales de l’institut Fourier

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We study the simultaneous linearizability of d –actions (and the corresponding d -dimensional Lie algebras) defined by commuting singular vector fields in ℂ n fixing the origin with nontrivial Jordan blocks in the linear parts. We prove the analytic convergence of the formal linearizing transformations under a certain invariant geometric condition for the spectrum of d vector fields generating a Lie algebra. If the condition fails and if we consider the situation where small denominators...

Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms

Viviane Baladi, Masato Tsujii (2007)

Annales de l’institut Fourier

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We study spectral properties of transfer operators for diffeomorphisms T : X → X on a Riemannian manifold X . Suppose that Ω is an isolated hyperbolic subset for T , with a compact isolating neighborhood V ⊂ X . We first introduce Banach spaces of distributions supported on V , which are anisotropic versions of the usual space of C p functions C p ( V ) and of the generalized Sobolev spaces W p , t ( V ) , respectively. We then show that the transfer operators associated to  T and a smooth weight g extend boundedly to these...

A.e. convergence of spectral sums on Lie groups

Christopher Meaney, Detlef Müller, Elena Prestini (2007)

Annales de l’institut Fourier

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Let ℒ be a right-invariant sub-Laplacian on a connected Lie group G , and let S R f : = ∫ 0 R d E λ f , R ≥ 0 , denote the associated “spherical partial sums,” where ℒ = ∫ 0 ∞ λ d E λ is the spectral resolution of ℒ . We prove that S R f ( x ) converges a.e. to f ( x ) as R → ∞ under the assumption log ( 2 + ℒ ) f ∈ L 2 ( G ) .

Analysis of joint spectral multipliers on Lie groups of polynomial growth

Alessio Martini (2012)

Annales de l’institut Fourier

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We study the problem of L p -boundedness ( 1 < p < ∞ ) of operators of the form m ( L 1 , ⋯ , L n ) for a commuting system of self-adjoint left-invariant differential operators L 1 , ⋯ , L n on a Lie group G of polynomial growth, which generate an algebra containing a weighted subcoercive operator. In particular, when G is a homogeneous group and L 1 , ⋯ , L n are homogeneous, we prove analogues of the Mihlin-Hörmander and Marcinkiewicz multiplier theorems.