Let C be a right-invariant sub-Laplacian on a connected Lie group G, and let S(R)f:= integral(R)(0) dE(lambda)f, R >= 0, denote the associated "spherical partial sums," where L = integral(infinity)(0) lambda dE(lambda) is the spectral resolution of L. We prove that S(R)f(x) converges a.e. to f(x) as R -> infinity under the assumption log(2 + L)f is an element of L-2(G).
Meaney, C., Muller, D., Prestini, E. (2007). A.e. convergence of spectral sums on Lie groups. ANNALES DE L'INSTITUT FOURIER, 57(5), 1509-1520.
A.e. convergence of spectral sums on Lie groups
PRESTINI, ELENA
2007-01-01
Abstract
Let C be a right-invariant sub-Laplacian on a connected Lie group G, and let S(R)f:= integral(R)(0) dE(lambda)f, R >= 0, denote the associated "spherical partial sums," where L = integral(infinity)(0) lambda dE(lambda) is the spectral resolution of L. We prove that S(R)f(x) converges a.e. to f(x) as R -> infinity under the assumption log(2 + L)f is an element of L-2(G).File in questo prodotto:
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