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Perturbation expansions for eigenvalues and eigenvectors for a rectangular membrane subject to a restorative force
Author(s):
Joyce
R.
McLaughlin;
Arturo
Portnoy
Journal:
Electron. Res. Announc. Amer. Math. Soc.
3
(1997),
72-77.
MSC (1991):
Primary 35P20
Posted:
August 19, 1997
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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.
References:
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- Ole H. Hald and Joyce R. McLaughlin, Inverse nodal problems: finding the potential from nodal lines, Memoirs of the American Mathematical Society, January 1996, Volume 119, Number 572. MR 97d:35240
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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:
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
Posted:
August 19, 1997
Communicated by:
Michael Taylor
Copyright of article:
Copyright
1997,
American Mathematical Society
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