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On the approximation of isolated eigenvalues of ordinary differential operators
Author(s):
Gerald
Teschl
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2473-2476.
MSC (2000):
Primary 34L40, 34L16;
Secondary 47N50, 34B20
Posted:
March 19, 2008
MathSciNet review:
2390515
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Abstract:
We extend a result of Stolz and Weidmann on the approximation of isolated eigenvalues of singular Sturm-Liouville and Dirac operators by the eigenvalues of regular operators.
References:
-
- 1.
- F. Gesztesy, B. Simon, and G. Teschl, Zeros of the Wronskian and renormalized oscillation theory, Amer. J. Math. 118, 571-594 (1996). MR 1393260 (97g:34105)
- 2.
- B. Simon, Trace Ideals and Their Applications, 2nd ed., Amer. Math. Soc., Providence, RI, 2005. MR 2154153 (2006f:47086)
- 3.
- G. Stolz and J. Weidmann, Approximation of isolated eigenvalues of ordinary differential operators, J. Reine und Angew. Math. 445, 31-44 (1993). MR 1244968 (95a:34122)
- 4.
- G. Stolz and J. Weidmann, Approximation of isolated eigenvalues of general singular ordinary differential operators, Results Math. 28, no. 3-4, 345-358 (1995). MR 1356897 (96j:34145)
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- 6.
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- 7.
- J. Weidmann, Spectral theory of Sturm-Liouville operators; approximation by regular problems, in Sturm-Liouville Theory: Past and Present (eds. W. Amrein, A. Hinz and D. Pearson), 75-98, Birkhäuser, Basel, 2005. MR 2145078
- 8.
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Additional Information:
Gerald
Teschl
Affiliation:
Faculty of Mathematics, Nordbergstrasse 15, 1090 Wien, Austria; and International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Wien, Austria
Email:
Gerald.Teschl@univie.ac.at
DOI:
10.1090/S0002-9939-08-09140-5
PII:
S 0002-9939(08)09140-5
Keywords:
Sturm--Liouville operators,
Dirac operators,
eigenvalues
Received by editor(s):
December 21, 2006,
Received by editor(s) in revised form:
February 26, 2007
Posted:
March 19, 2008
Additional Notes:
This research was supported by the Austrian Science Fund (FWF) under Grant No. Y330
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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