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- Title
Topics on the spectral properties of degenerate non-self-adjoint differential operators.
- Authors
Sameripour, Ali; Yadollahi, Yousef
- Abstract
Let $( Pu ) ( t ) =- \frac{d}{dt} ( \omega^{2} ( t ) q ( t ) \frac{du ( t )}{dt} )$ be a degenerate non-self-adjoint operator defined on the space $H_{\ell} = L^{2} (0,1)^{\ell}$ with Dirichlet-type boundary conditions, where $\omega(t)\in C^{1} (0,1)$ is a positive function with further assumptions that will be specified later, and $q(t)\in C^{2} ( [ 0,1 ], \operatorname{End} C^{\ell} )$ is a matrix function. In this article, some spectral characteristics of the operator P are considered. We estimate the resolvent of P and then prove the limit argument theorem. Finally, we find a formula for the distribution of eigenvalues of the operator P acting on $H_{\ell}$ .
- Subjects
NONSELFADJOINT operators; BOUNDARY value problems; MATRIX functions; EIGENVALUES; RESOLVENTS (Mathematics)
- Publication
Journal of Inequalities & Applications, 2016, Vol 2016, Issue 1, p1
- ISSN
1025-5834
- Publication type
Article
- DOI
10.1186/s13660-016-1138-5