On Perturbation of Operators and Rayleigh-Schrödinger Coefficients
(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:
https://lup.lub.lu.se/record/3b8e4946-d290-4148-ae25-74897bca0979
- author
- Carlsson, Marcus LU and Rubin, Olof LU
- organization
- publishing date
- 2024-04
- 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}}, }