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

[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.

[发布日期] 2015-12-15

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