Perturbations of embedded eigenvalues for self-adjoint ODE systems
(2023) In Arkiv for Matematik 61(1). p.177-202- Abstract
We consider a perturbation problem for embedded eigenvalues of a self-adjoint differential operator in L2(R;Rn). In particular, we study the set of all small perturbations in an appropriate Banach space for which the embedded eigenvalue remains embedded in the continuous spectrum. We show that this set of small perturbations forms a smooth manifold and we specify its co-dimension. Our methods involve the use of exponential dichotomies, their roughness property and Lyapunov-Schmidt reduction.
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https://lup.lub.lu.se/record/db0a3eca-3877-493e-8fc4-e0e9acbbb053
- author
- Sasane, Sara Maad LU and Papalazarou, Alexia LU
- organization
- publishing date
- 2023
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Arkiv for Matematik
- volume
- 61
- issue
- 1
- pages
- 26 pages
- publisher
- Springer
- external identifiers
-
- scopus:85159200775
- ISSN
- 0004-2080
- DOI
- 10.4310/ARKIV.2023.v61.n1.a9
- language
- English
- LU publication?
- yes
- id
- db0a3eca-3877-493e-8fc4-e0e9acbbb053
- date added to LUP
- 2023-08-15 09:30:14
- date last changed
- 2023-11-22 21:05:25
@article{db0a3eca-3877-493e-8fc4-e0e9acbbb053, abstract = {{<p>We consider a perturbation problem for embedded eigenvalues of a self-adjoint differential operator in L<sup>2</sup>(R;R<sup>n</sup>). In particular, we study the set of all small perturbations in an appropriate Banach space for which the embedded eigenvalue remains embedded in the continuous spectrum. We show that this set of small perturbations forms a smooth manifold and we specify its co-dimension. Our methods involve the use of exponential dichotomies, their roughness property and Lyapunov-Schmidt reduction.</p>}}, author = {{Sasane, Sara Maad and Papalazarou, Alexia}}, issn = {{0004-2080}}, language = {{eng}}, number = {{1}}, pages = {{177--202}}, publisher = {{Springer}}, series = {{Arkiv for Matematik}}, title = {{Perturbations of embedded eigenvalues for self-adjoint ODE systems}}, url = {{http://dx.doi.org/10.4310/ARKIV.2023.v61.n1.a9}}, doi = {{10.4310/ARKIV.2023.v61.n1.a9}}, volume = {{61}}, year = {{2023}}, }