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

Published online by Cambridge University Press:  02 June 2020

Da-Wen Deng
Affiliation:
Hunan Key Laboratory for Computational and Simulation in Science and Engineering, School of Mathematics and Computational Sciences, Xiangtan University, Hunan411105, People's Republic of China (taimantang@gmail.com; tmtang@xtu.edu.cn)
Sze-Man Ngai
Affiliation:
Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan410081, People's Republic of China Department of Mathematical Sciences, Georgia Southern University, StatesboroGA30460-8093, USA (smngai@georgiasouthern.edu)

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.

Type
Research Article
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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