no. 5
A.e. convergence of spectral sums on Lie groups
[Convergence p.p. de sommes spectrales sur les groupes de Lie]
Meaney, Christopher1 ; Müller, Detlef2 ; Prestini, Elena3
1 Macquarie University Department of Mathematics North Ryde NSW 2109 (Australia)
2 C.A.-Universität Kiel Mathematisches Seminar Ludewig-Meyn-Str.4 D-24098 Kiel (Germany)
3 Università di Roma “Tor Vergata" Dipartimento di Matematica Via della Ricerca Scientifica 00133 Roma (Italie)
Annales de l'Institut Fourier, Tome 57 (2007) no. 5, pp. 1509-1520.

Soit ℒ un sous-Laplacien invariant à droite sur un groupe de Lie G, et soit S R f:=∫ 0 R dE λ f,R≥0, l’opérateur “sommes sphériques partielles” associé, où ℒ=∫ 0 ∞ λdE λ dénote la résolution spectrale de ℒ. Nous prouvons que S R f(x) converge vers f(x) p.p. quand R→∞, si log(2+ℒ)f∈L 2 (G).

Let ℒ be a right-invariant sub-Laplacian on a connected Lie group G, and let S R f:=∫ 0 R dE λ f,R≥0, denote the associated “spherical partial sums,” where ℒ=∫ 0 ∞ λdE 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).

DOI : 10.5802/aif.2303
Classification : 22E30, 43A50
Keywords: Rademacher-Menshov theorem, sub-Laplacian, spectral theory
Mot clés : théorème de Rademacher-Menchov, sous-Laplacien, théorie spectrale

Meaney, Christopher 1 ; Müller, Detlef 2 ; Prestini, Elena 3

1 Macquarie University Department of Mathematics North Ryde NSW 2109 (Australia)
2 C.A.-Universität Kiel Mathematisches Seminar Ludewig-Meyn-Str.4 D-24098 Kiel (Germany)
3 Università di Roma “Tor Vergata" Dipartimento di Matematica Via della Ricerca Scientifica 00133 Roma (Italie) 
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     title = {A.e. convergence of spectral sums on {Lie} groups},
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Meaney, Christopher; Müller, Detlef; Prestini, Elena. A.e. convergence of spectral sums on Lie groups. Annales de l'Institut Fourier, Tome 57 (2007) no. 5, pp. 1509-1520. doi : 10.5802/aif.2303. https://aif.centre-mersenne.org/articles/10.5802/aif.2303/

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