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

Da-Wen Deng Xiangtan University Sze-Man Ngai Georgia Southern University and Hunan Normal University

Publications of CMSA of Harvard mathscidoc:1901.38001

For Laplacians defined by measures on a bounded domain in R^n, we prove analogs 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, Polya and Weinberger. This work is motivated by the study of spectral gaps for Laplacians on fractals.
Eigenvalue estimate; Fractal; measure; Laplacian
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@inproceedings{da-wenestimates,
  title={Estimates for sums and gaps of eigenvalues of Laplacians on measure spaces},
  author={Da-Wen Deng, and Sze-Man Ngai},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190121024604597809193},
}
Da-Wen Deng, and Sze-Man Ngai. Estimates for sums and gaps of eigenvalues of Laplacians on measure spaces. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190121024604597809193.
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