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On Perturbation of Operators and Rayleigh-Schrödinger Coefficients

Carlsson, Marcus LU and Rubin, Olof LU orcid (2024) In Complex Analysis and Operator Theory 18(3).
Abstract

Let A and E be self-adjoint matrices or operators on ℓ2(N), where A is fixed and E is a small perturbation. We study how the eigenvalues of A+E depend on E, with the aim of obtaining second order formulas that are explicitly computable in terms of the spectral decomposition of A and a certain block decomposition of E. In particular we extend the classical Rayleigh-Schrödinger formulas for the one-parameter perturbation A+tE where t∈R varies and E is held fixed, by dropping t and considering E as the variable.

Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
15A18, 15B57, 47A10, 47A55, 47B15, Eigenvalue expansion, Perturbation of Hermitian operators
in
Complex Analysis and Operator Theory
volume
18
issue
3
article number
47
publisher
Springer
external identifiers
  • scopus:85186890516
ISSN
1661-8254
DOI
10.1007/s11785-024-01482-9
language
English
LU publication?
yes
id
3b8e4946-d290-4148-ae25-74897bca0979
date added to LUP
2024-03-27 14:17:01
date last changed
2024-03-27 14:17:29
@article{3b8e4946-d290-4148-ae25-74897bca0979,
  abstract     = {{<p>Let A and E be self-adjoint matrices or operators on ℓ<sup>2</sup>(N), where A is fixed and E is a small perturbation. We study how the eigenvalues of A+E depend on E, with the aim of obtaining second order formulas that are explicitly computable in terms of the spectral decomposition of A and a certain block decomposition of E. In particular we extend the classical Rayleigh-Schrödinger formulas for the one-parameter perturbation A+tE where t∈R varies and E is held fixed, by dropping t and considering E as the variable.</p>}},
  author       = {{Carlsson, Marcus and Rubin, Olof}},
  issn         = {{1661-8254}},
  keywords     = {{15A18; 15B57; 47A10; 47A55; 47B15; Eigenvalue expansion; Perturbation of Hermitian operators}},
  language     = {{eng}},
  number       = {{3}},
  publisher    = {{Springer}},
  series       = {{Complex Analysis and Operator Theory}},
  title        = {{On Perturbation of Operators and Rayleigh-Schrödinger Coefficients}},
  url          = {{http://dx.doi.org/10.1007/s11785-024-01482-9}},
  doi          = {{10.1007/s11785-024-01482-9}},
  volume       = {{18}},
  year         = {{2024}},
}