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Asymptotics for the spectral heat function and bounds for integrals of Dirichlet eigenfunctions
Published online by Cambridge University Press: 14 November 2011
Extract
We introduce the spectral heat function H associated with the Dirichlet-Laplace–Beltrami operator ΔM on a compact smooth Riemannian manifold M with a non-empty smooth boundary. We obtain two-term asymptotics for H without assuming any billiard conditions on M. As a corollary, we obtain estimates for the integral of the k′th Dirichlet eigenfunction of ΔM over M for k→∞.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 129 , Issue 4 , 1999 , pp. 841 - 854
- Copyright
- Copyright © Royal Society of Edinburgh 1999
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