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eigenvalue estimate

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Estimates for sums and gaps of eigenvalues of Laplacians on measure spaces
Part of
Da-Wen Deng, Sze-Man Ngai
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 151 / Issue 2 / April 2021

Published online by Cambridge University Press:

02 June 2020, pp. 842-861

Print publication:

April 2021
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For Laplacians defined by measures on a bounded domain in ℝn, we prove analogues of the classical eigenvalue estimates for the standard Laplacian: lower bound of sums of eigenvalues by Li and Yau, and gaps of consecutive eigenvalues by Payne, Pólya and Weinberger. This work is motivated by the study of spectral gaps for Laplacians on fractals.