Geodesic
Perturbation expansions for eigenvalues and eigenvectors for a rectangular membrane subject to a restorative force
McLaughlin, Joyce1 ; Portnoy, Arturo1
1 Rensselaer Polytechnic Institute, Troy, NY 12180
Electronic research announcements of the American Mathematical Society, Tome 03 (1997), pp. 72-77 Cet article a éte moissonné depuis la source American Mathematical Society

Voir la notice de l'article

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.
DOI : 10.1090/S1079-6762-97-00027-9

McLaughlin, Joyce 1 ; Portnoy, Arturo 1

1 Rensselaer Polytechnic Institute, Troy, NY 12180 
@article{10_1090_S1079_6762_97_00027_9,
     author = {McLaughlin, Joyce and Portnoy, Arturo},
     title = {Perturbation expansions for eigenvalues and eigenvectors for a rectangular membrane subject to a restorative force},
     journal = {Electronic research announcements of the American Mathematical Society},
     pages = {72--77},
     year = {1997},
     volume = {03},
     doi = {10.1090/S1079-6762-97-00027-9},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-97-00027-9/}
}
TY  - JOUR
AU  - McLaughlin, Joyce
AU  - Portnoy, Arturo
TI  - Perturbation expansions for eigenvalues and eigenvectors for a rectangular membrane subject to a restorative force
JO  - Electronic research announcements of the American Mathematical Society
PY  - 1997
SP  - 72
EP  - 77
VL  - 03
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-97-00027-9/
DO  - 10.1090/S1079-6762-97-00027-9
ID  - 10_1090_S1079_6762_97_00027_9
ER  - 
%0 Journal Article
%A McLaughlin, Joyce
%A Portnoy, Arturo
%T Perturbation expansions for eigenvalues and eigenvectors for a rectangular membrane subject to a restorative force
%J Electronic research announcements of the American Mathematical Society
%D 1997
%P 72-77
%V 03
%U http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-97-00027-9/
%R 10.1090/S1079-6762-97-00027-9
%F 10_1090_S1079_6762_97_00027_9
McLaughlin, Joyce; Portnoy, Arturo. Perturbation expansions for eigenvalues and eigenvectors for a rectangular membrane subject to a restorative force. Electronic research announcements of the American Mathematical Society, Tome 03 (1997), pp. 72-77. doi: 10.1090/S1079-6762-97-00027-9

[1] Hald, Ole H., Mclaughlin, Joyce R. Inverse nodal problems: finding the potential from nodal lines Mem. Amer. Math. Soc. 1996

[2] Mclaughlin, Joyce R., Hald, Ole H. A formula for finding a potential from nodal lines Bull. Amer. Math. Soc. (N.S.) 1995 241 247

[3] Feldman, Joel, Knörrer, Horst, Trubowitz, Eugene The perturbatively stable spectrum of a periodic Schrödinger operator Invent. Math. 1990 259 300

[4] Friedlander, Leonid On the spectrum of the periodic problem for the Schrödinger operator Comm. Partial Differential Equations 1990 1631 1647

[5] Karpeshina, Yu. E. Analytic perturbation theory for a periodic potential Izv. Akad. Nauk SSSR Ser. Mat. 1989 45 65

[6] Karpeshina, Yu. E. Geometrical background for the perturbation theory of the polyharmonic operator with periodic potentials 1989 251 276

[7] Kato, Tosio Perturbation theory for linear operators 1976

[8] Schmidt, Wolfgang M. Diophantine approximations and Diophantine equations 1991

[9] Taylor, Angus Ellis, Lay, David C. Introduction to functional analysis 1980

Cité par Sources :