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On almost-everywhere convergent eigenfunction expansions of the Laplace–Beltrami operator

Published online by Cambridge University Press:  24 October 2008

Christopher Meaney
Christopher Meaney
Affiliation:
University of Adelaide
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 1 , July 1982 , pp. 129 - 131
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

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