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A.e. convergence of spectral sums on Lie groups

Christopher MeaneyDetlef MüllerElena Prestini — 2007

Annales de l’institut Fourier

Let be a right-invariant sub-Laplacian on a connected Lie group G , and let S R f : = 0 R d E λ f , R 0 , denote the associated “spherical partial sums,” where = 0 λ d E 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 + ) f L 2 ( G ) .

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