Estimates for sums and gaps of eigenvalues of Laplacians on measure spaces

Da Wen Deng; Sze Man Ngai

doi:10.1017/prm.2020.39

Estimates for sums and gaps of eigenvalues of Laplacians on measure spaces

Da Wen Deng, Sze Man Ngai

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	842-861
Number of pages	20
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume	151
Issue number	2
DOIs	https://doi.org/10.1017/prm.2020.39
State	Published - Apr 2021

Keywords

Eigenvalue estimate
Fractal
Laplacian
Measure

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10.1017/prm.2020.39

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Estimates for sums and gaps of eigenvalues of Laplacians on measure spaces

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Keywords

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