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ISSN 1079-6762

Perturbation expansions for eigenvalues and eigenvectors for a rectangular membrane subject to a restorative force


Authors: Joyce R. McLaughlin and Arturo Portnoy
Journal: Electron. Res. Announc. Amer. Math. Soc. 3 (1997), 72-77
MSC (1991): Primary 35P20
Published electronically: August 19, 1997
MathSciNet review: 1461976
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Abstract: Series expansions are obtained for a rich subset of eigenvalues and eigenfunctions of an operator that arises in the study of rectangular membranes: the operator is the 2-D Laplacian with restorative force term and Dirichlet boundary conditions. Expansions are extracted by considering the restorative force term as a linear perturbation of the Laplacian; errors of truncation for these expansions are estimated. The criteria defining the subset of eigenvalues and eigenfunctions that can be studied depend only on the size and linearity of the perturbation. The results are valid for almost all rectangular domains.


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Additional Information

Joyce R. McLaughlin
Affiliation: Rensselaer Polytechnic Institute, Troy, NY 12180
Email: mclauj@rpi.edu

Arturo Portnoy
Affiliation: Rensselaer Polytechnic Institute, Troy, NY 12180
Email: portna@rpi.edu

DOI: http://dx.doi.org/10.1090/S1079-6762-97-00027-9
PII: S 1079-6762(97)00027-9
Keywords: Perturbation expansion, eigenvalue, eigenvector, membrane, inverse nodal problem
Received by editor(s): May 16, 1997
Published electronically: August 19, 1997
Communicated by: Michael Taylor
Article copyright: © Copyright 1997 American Mathematical Society