The aim of this article is to present a simple proof of the theorem about perturbation of the Sturm-Liouville operator in Liouville normal form.
@article{bwmeta1.element.bwnjournal-article-bcpv38i1p183bwm, author = {Kosowski, Przemys\L aw}, title = {A simple proof of the spectral continuity of the Sturm-Liouville problem}, journal = {Banach Center Publications}, volume = {38}, year = {1997}, pages = {183-186}, zbl = {0878.34017}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv38i1p183bwm} }
Kosowski, PrzemysŁaw. A simple proof of the spectral continuity of the Sturm-Liouville problem. Banach Center Publications, Tome 38 (1997) pp. 183-186. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv38i1p183bwm/
[000] [1] G. Birkhoff and G.-C. Rota, Ordinary Differential Equations, Ginn-Blaisdell, Boston, 1962. | Zbl 0102.29901
[001] [2] R. Courant and D. Hilbert, Methods of Mathematical Physics, vol. 1, Interscience, New York, 1953. | Zbl 0051.28802
[002] [3] C. T. Fulton and S. Pruess, Eigenvalue and eigenfunction asymptotics for regular Sturm-Liouville problems, J. Math. Anal. Appl. 188 (1994), 297-340. | Zbl 0812.34073
[003] [4] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1966.
[004] [5] B. M. Levitan and I. S. Sargsyan, Sturm-Liouville and Dirac Operators, Kluwer, Dordrecht, 1991.
[005] [6] J. D. Pryce, Numerical Solution of Sturm-Liouville Problems, Clarendon Press, New York, 1993. | Zbl 0795.65053
[006] [7] M. H. Stone, Linear Transformations in Hilbert Space, American Mathematical Society, New York, 1932.