A simple proof of the spectral continuity of the Sturm-Liouville problem

PrzemysŁaw Kosowski

Banach Center Publications (1997)

  • Volume: 38, Issue: 1, page 183-186
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Kosowski, PrzemysŁaw. "A simple proof of the spectral continuity of the Sturm-Liouville problem." Banach Center Publications 38.1 (1997): 183-186. <http://eudml.org/doc/208626>.

@article{Kosowski1997,
abstract = {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.},
author = {Kosowski, PrzemysŁaw},
journal = {Banach Center Publications},
keywords = {spectral continuity; perturbation; Sturm-Liouville operator; Liouville normal},
language = {eng},
number = {1},
pages = {183-186},
title = {A simple proof of the spectral continuity of the Sturm-Liouville problem},
url = {http://eudml.org/doc/208626},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Kosowski, PrzemysŁaw
TI - A simple proof of the spectral continuity of the Sturm-Liouville problem
JO - Banach Center Publications
PY - 1997
VL - 38
IS - 1
SP - 183
EP - 186
AB - 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.
LA - eng
KW - spectral continuity; perturbation; Sturm-Liouville operator; Liouville normal
UR - http://eudml.org/doc/208626
ER -

References

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  1. [1] G. Birkhoff and G.-C. Rota, Ordinary Differential Equations, Ginn-Blaisdell, Boston, 1962. Zbl0102.29901
  2. [2] R. Courant and D. Hilbert, Methods of Mathematical Physics, vol. 1, Interscience, New York, 1953. Zbl0051.28802
  3. [3] C. T. Fulton and S. Pruess, Eigenvalue and eigenfunction asymptotics for regular Sturm-Liouville problems, J. Math. Anal. Appl. 188 (1994), 297-340. Zbl0812.34073
  4. [4] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1966. 
  5. [5] B. M. Levitan and I. S. Sargsyan, Sturm-Liouville and Dirac Operators, Kluwer, Dordrecht, 1991. 
  6. [6] J. D. Pryce, Numerical Solution of Sturm-Liouville Problems, Clarendon Press, New York, 1993. Zbl0795.65053
  7. [7] M. H. Stone, Linear Transformations in Hilbert Space, American Mathematical Society, New York, 1932. 

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