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On almost-everywhere convergent eigenfunction expansions of the Laplace–Beltrami operator
Published online by Cambridge University Press: 24 October 2008
Abstract
Let M be a compact Riemannian manifold equipped with Laplace–Beltrami operator Δ. We use the Rademacher-Menchoff theorem and the asymptotics of the eigenvalues of Δ to show that if a function belongs to an L2 Sobolev space of positive index then its expansion, in terms of eigenfunctions of Δ, converges almost everywhere on M.
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- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 1 , July 1982 , pp. 129 - 131
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- Copyright © Cambridge Philosophical Society 1982
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