A.e. convergence of spectral sums on Lie groups
Annales de l'Institut Fourier, Volume 57 (2007) no. 5, pp. 1509-1520.

Let be a right-invariant sub-Laplacian on a connected Lie group G, and let S R f:= 0 R dE λ f,R0, denote the associated “spherical partial sums,” where = 0 λdE λ is the spectral resolution of . We prove that S R f(x) converges a.e. to f(x) as R under the assumption log(2+)fL 2 (G).

Soit un sous-Laplacien invariant à droite sur un groupe de Lie G, et soit S R f:= 0 R dE λ f,R0, l’opérateur “sommes sphériques partielles” associé, où = 0 λdE λ dénote la résolution spectrale de . Nous prouvons que S R f(x) converge vers f(x) p.p. quand R, si log(2+)fL 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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Meaney, Christopher; Müller, Detlef; Prestini, Elena. A.e. convergence of spectral sums on Lie groups. Annales de l'Institut Fourier, Volume 57 (2007) no. 5, pp. 1509-1520. doi : 10.5802/aif.2303. http://archive.numdam.org/articles/10.5802/aif.2303/

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