Analysis of joint spectral multipliers on Lie groups of polynomial growth

Alessio Martini

Displaying similar documents to “Analysis of joint spectral multipliers on Lie groups of polynomial growth”

Multiplier theorem on generalized Heisenberg groups II

Waldemar Hebisch, Jacek Zienkiewicz (1996)

Colloquium Mathematicae

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We prove that on a product of generalized Heisenberg groups, a Hörmander type multiplier theorem for Rockland operators is true with the critical index n/2 + ϵ, ϵ>0, where n is the euclidean (topological) dimension of the group.

Multiplier theorem on generalized Heisenberg groups

Waldemar Hebisch (1993)

Colloquium Mathematicae

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Gelfand transforms of $S O (3)$ -invariant Schwartz functions on the free group $N_{3, 2}$

Véronique Fischer, Fulvio Ricci (2009)

Annales de l’institut Fourier

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The spectrum of a Gelfand pair $(K ⋉ N, K)$ , where $N$ is a nilpotent group, can be embedded in a Euclidean space. We prove that in general, the Schwartz functions on the spectrum are the Gelfand transforms of Schwartz $K$ -invariant functions on $N$ . We also show the converse in the case of the Gelfand pair $(S O (3) ⋉ N_{3, 2}, S O (3))$ , where $N_{3, 2}$ is the free two-step nilpotent Lie group with three generators. This extends recent results for the Heisenberg group.

Semi-classical functional calculus on manifolds with ends and weighted $L^{p}$ estimates

Jean-Marc Bouclet (2011)

Annales de l’institut Fourier

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For a class of non compact Riemannian manifolds with ends, we give semi-classical expansions of bounded functions of the Laplacian. We then study related $L^{p}$ boundedness properties of these operators and show in particular that, although they are not bounded on $L^{p}$ in general, they are always bounded on suitable weighted $L^{p}$ spaces.

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 $S_{R} f : = \int_{0}^{R} d E_{λ} f, R \geq 0,$ denote the associated “spherical partial sums,” where $ℒ = \int_{0}^{\infty} λ d E_{λ}$ is the spectral resolution of $ℒ .$ We prove that $S_{R} f (x)$ converges a.e. to $f (x)$ as $R \to \infty$ under the assumption $log (2 + ℒ) f \in L^{2} (G) .$

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 $T : X \to X$ on a Riemannian manifold $X$ . Suppose that $Ω$ is an isolated hyperbolic subset for $T$ , with a compact isolating neighborhood $V \subset X$ . 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...

Displaying similar documents to “Analysis of joint spectral multipliers on Lie groups of polynomial growth”

Multiplier theorem on generalized Heisenberg groups II

Multiplier theorem on generalized Heisenberg groups

Gelfand transforms of S O ( 3 ) -invariant Schwartz functions on the free group N 3 , 2

Semi-classical functional calculus on manifolds with ends and weighted L p estimates

A.e. convergence of spectral sums on Lie groups

Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms

Gelfand transforms of $S O (3)$ -invariant Schwartz functions on the free group $N_{3, 2}$

Semi-classical functional calculus on manifolds with ends and weighted $L^{p}$ estimates