Spectral deformations and exponential decay of eigenfunctions for the Neumann Laplacian on manifolds with quasicylindrical ends

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:432

Article

Kalvin, Victor

关键词: Embedded eigenvalues;    Eigenfunction decay;    Eigenvalue accumulation;    Complex scaling;    Analytic dilations;    Perfectly matched layer;   

DOI  :  10.1016/j.jmaa.2015.07.008

来源: Elsevier

【 摘 要 】

We study spectral properties of the Neumann Laplacian on manifolds with quasicylindrical ends. In particular, we prove exponential decay of the non-threshold eigenfunctions and show that the eigenvalues can accumulate only at thresholds of the absolutely continuous spectrum and only from below. The non-threshold eigenvalues are also discrete eigenvalues of a non-selfadjoint operator. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free