On G-convergence of positive Self-adjoint operators

We apply G-convergence theory to study the asymptotic of the eigenvalue problems of positive definite bounded self-adjoint \(h\)-dependent operators as \(h\to\infty\). Two operators are considered; a second order elliptic operator and a general linear operator. Using the definition of G-convergence...

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Bibliographic Details
Published in:arXiv.org 2019-10
Main Authors: Almanasreh, Hasan, Shalalfeh, Mahmoud
Format: Article
Language:English
Subjects:
Convergence
Eigenvalues
Linear operators
Quadratic forms
Online Access:Get full text
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Summary:We apply G-convergence theory to study the asymptotic of the eigenvalue problems of positive definite bounded self-adjoint \(h\)-dependent operators as \(h\to\infty\). Two operators are considered; a second order elliptic operator and a general linear operator. Using the definition of G-convergence of elliptic operator, we review convergence results of the elliptic eigenvalue problem as \(h\to\infty\). Also employing the general definition of G-convergence of positive definite self-adjoint operator together with \(\Gamma\)-convergence of the associated quadratic form, we characterize the G-limit as \(h\to\infty\) of the general operator with some classes of perturbations. As a consequence, we also prove the convergence of the corresponding spectrum.
ISSN:2331-8422