Upper and lower bounds for normal derivatives of spectral clusters of Dirichlet Laplacian

Xiangjin Xu

doi:10.1016/j.jmaa.2011.09.003

Upper and lower bounds for normal derivatives of spectral clusters of Dirichlet Laplacian

Xiangjin Xu

Mathematics and Statistics

Binghamton University

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

6 Scopus citations

Abstract

In this paper, we prove the upper and lower bounds for normal derivatives of spectral clusters u=χλsf of Dirichlet Laplacian δ_M, where the upper bound is true for any Riemannian manifold, and the lower bound is true for some small 0<s<s_M, where s_M depends on the manifold only, provided that M has no trapped geodesics (see Theorem 1.3 for a precise statement), which generalizes the early results for single eigenfunctions by Hassell and Tao in 2002.

Original language	English
Pages (from-to)	374-383
Number of pages	10
Journal	Journal of Mathematical Analysis and Applications
Volume	387
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2011.09.003
State	Published - Mar 1 2012

Keywords

Dirichlet Laplacian
No trapped geodesics
Normal derivatives
Spectral cluster

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10.1016/j.jmaa.2011.09.003

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abstract = "In this paper, we prove the upper and lower bounds for normal derivatives of spectral clusters u=χλsf of Dirichlet Laplacian δM, where the upper bound is true for any Riemannian manifold, and the lower bound is true for some small 0M, where sM depends on the manifold only, provided that M has no trapped geodesics (see Theorem 1.3 for a precise statement), which generalizes the early results for single eigenfunctions by Hassell and Tao in 2002.",

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AB - In this paper, we prove the upper and lower bounds for normal derivatives of spectral clusters u=χλsf of Dirichlet Laplacian δM, where the upper bound is true for any Riemannian manifold, and the lower bound is true for some small 0M, where sM depends on the manifold only, provided that M has no trapped geodesics (see Theorem 1.3 for a precise statement), which generalizes the early results for single eigenfunctions by Hassell and Tao in 2002.

KW - Dirichlet Laplacian

KW - No trapped geodesics

KW - Normal derivatives

KW - Spectral cluster

UR - https://www.scopus.com/pages/publications/80054059073

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DO - 10.1016/j.jmaa.2011.09.003

M3 - Article

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VL - 387

SP - 374

EP - 383

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Upper and lower bounds for normal derivatives of spectral clusters of Dirichlet Laplacian

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Keywords

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