Communications in Mathematical Physics

, Volume 345, Issue 2, pp 615–630 | Cite as

Approximations of Strongly Continuous Families of Unbounded Self-Adjoint Operators

  • Jonathan Ben-ArtziEmail author
  • Thomas Holding
Open Access


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.


Discrete Spectrum Essential Spectrum Continuous Family Maxwell System Compact Resolvent 
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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of MathematicsImperial College LondonLondonUK
  2. 2.Cambridge Centre for AnalysisUniversity of CambridgeCambridgeUK

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