A.e. convergence of spectral sums on Lie groups
Annales de l'Institut Fourier, Volume 57 (2007) no. 5, p. 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 : https://doi.org/10.5802/aif.2303
Classification:  22E30,  43A50
Keywords: Rademacher-Menshov theorem, sub-Laplacian, spectral theory
@article{AIF_2007__57_5_1509_0,
     author = {Meaney, Christopher and M\"uller, Detlef and Prestini, Elena},
     title = {A.e. convergence of spectral sums on Lie groups},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {57},
     number = {5},
     year = {2007},
     pages = {1509-1520},
     doi = {10.5802/aif.2303},
     zbl = {1131.22007},
     mrnumber = {2364139},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2007__57_5_1509_0}
}
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. https://aif.centre-mersenne.org/item/AIF_2007__57_5_1509_0/

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