A.e. convergence of spectral sums on Lie groups

Authors:

CMChristopher Meaney
Christopher Meaney
DMDetlef Müller
Detlef Müller
EPElena Prestini
Elena Prestini

Publisher website

1 January 2007

journal article
Published by MathDoc/Centre Mersenne in Annales de l'institut Fourier

Vol. 57 (5) , 1509-1520
DOI:10.5802/aif.2303

Abstract

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) .

Keywords

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