Approximations of strongly continuous families of unbounded self-adjoint operators

Ben-Artzi, Jonathan ORCID: https://orcid.org/0000-0001-6184-9313 and Holding, Thomas 2016. Approximations of strongly continuous families of unbounded self-adjoint operators. Communications in Mathematical Physics 345 , pp. 615-630. 10.1007/s00220-016-2637-4

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Abstract

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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Additional Information:	This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), 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.
Publisher:	Springer Verlag
ISSN:	0010-3616
Date of First Compliant Deposit:	23 September 2016
Date of Acceptance:	11 February 2016
Last Modified:	06 May 2023 04:26
URI:	https://orca.cardiff.ac.uk/id/eprint/94808

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