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Perturbations of embedded eigenvalues for self-adjoint ODE systems

Sasane, Sara Maad LU and Papalazarou, Alexia LU (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.

Please use this url to cite or link to this publication:
author
and
organization
publishing date
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}},
}