Given two self-adjoint operators A and V = V + -V -, we study the motion of the eigenvalues of the operator A t = A -tV as t increases. Let Ξ± > 0 and let Ξ» be a regular point for A. We consider the quantities N + V Ξ» Ξ± , N -V Ξ» Ξ± , and N 0 V Ξ» Ξ± defined as the number of eigenvalues of the operator A
Discrete spectrum in the gaps for perturbations of periodic Jacobi matrices
β Scribed by P.A. Cojuhari
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 736 KB
- Volume
- 225
- Category
- Article
- ISSN
- 0377-0427
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π SIMILAR VOLUMES
It is proved that small periodic singular perturbation of a cylindrical waveguide surface may open a gap in the essential spectrum of the Dirichlet problem for the Laplace operator. If the perturbation period is long and the caverns in the cylinder are small, the gap certainly opens.
## Abstract We consider the buckling problem for a family of thin plates with thickness parameter __Ξ΅__. This involves finding the least positive multiple __Ξ»__ of the load that makes the plate __buckle__, a value that can be expressed in terms of an eigenvalue problem involving a nonβcompact opera