Perturbation behavior of a multiple eigenvalue in
β Scribed by Yuji Nakatsukasa
- Publisher
- Springer Netherlands
- Year
- 2010
- Tongue
- English
- Weight
- 393 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0006-3835
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## Abstract We consider a nonβcompact Riemannian periodic manifold such that the corresponding Laplacian has a spectral gap. By continuously perturbing the periodic metric locally we can prove the existence of eigenvalues in a gap. A lower bound on the number of eigenvalue branches crossing a fixed
be Hermitian matrices with eigenvalues Ξ» 1 β’ β’ β’ Ξ» k and Ξ» 1 β’ β’ β’ Ξ» k , respectively. Denote by E the spectral norm of the matrix E, and Ξ· the spectral gap between the spectra of H 1 and H 2 . It is shown that , which improves all the existing results. Similar bounds are obtained for singular valu