Approximations of Strongly Continuous Families of Unbounded Self-Adjoint Operators

被引：0
作者：
Jonathan Ben-Artzi
Thomas Holding
机构：
[1] Imperial College London,Department of Mathematics
[2] University of Cambridge,Cambridge Centre for Analysis
来源：
Communications in Mathematical Physics | 2016年 / 345卷
关键词：
Discrete Spectrum; Essential Spectrum; Continuous Family; Maxwell System; Compact Resolvent;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The problem of approximating the discrete spectra of families of self-adjoint operators that are merely strongly continuous is addressed. It is well-known that the spectrum need not vary continuously (as a set) under strong perturbations. However, it is shown that under an additional compactness assumption the spectrum does vary continuously, and a family of symmetric finite-dimensional approximations is constructed. An important feature of these approximations is that they are valid for the entire family uniformly. An application of this result to the study of plasma instabilities is illustrated.
引用
收藏
页码：615 / 630
页数：15
相关论文
共 19 条
  • [1] Ben-Artzi J.(2011)Instability of nonsymmetric nonmonotone equilibria of the Vlasov–Maxwell system J. Math. Phys. 52 123703-169
  • [2] Curtis C.W.(2010)On the convergence of Hills method Math. Comput. 79 169-438
  • [3] Deconinck B.(2004)Spectral pollution IMA J. Numer. Anal. 24 417-321
  • [4] Davies E.B.(2006)Computing spectra of linear operators using the Floquet–Fourier–Hill method J. Comput. Phys. 219 296-2126
  • [5] Plum M.(2008)On the approximation of spectra of linear operators on Hilbert spaces J. Funct. Anal. 254 2092-78
  • [6] Deconinck B.(2012)Convergence of Hill’s Method for Nonselfadjoint Operators SIAM J. Numer. Anal. 50 64-224
  • [7] Kutz J.N.(2014)Perturbation of operators and approximation of spectrum Proc. Math. Sci. 124 205-416
  • [8] Hansen A.C.(2004)Spectral pollution and second-order relative spectra for self-adjoint operators IMA J. Numer. Anal. 24 393-900
  • [9] Johnson M.A.(2009)Spectral pollution and how to avoid it Proc. Lond. Math. Soc. 100 864-320
  • [10] Zumbrun K.(1991)Fifty years of eigenvalue perturbation theory Bull. Am. Math. Soc. 24 303-3103
12