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Bound states of discrete Schrödinger operators with super-critical inverse square potentials
Author(s):
David
Damanik;
Gerald
Teschl
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1123-1127.
MSC (2000):
Primary 47B36, 81Q10;
Secondary 39A11, 47B39
Posted:
October 4, 2006
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Abstract:
We consider discrete one-dimensional Schrödinger operators whose potentials decay asymptotically like an inverse square. In the super-critical case, where there are infinitely many discrete eigenvalues, we compute precise asymptotics of the number of eigenvalues below a given energy  as this energy tends to the bottom of the essential spectrum.
References:
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Additional Information:
David
Damanik
Affiliation:
Mathematics 253--37, California Institute of Technology, Pasadena, California 91125
Email:
damanik@caltech.edu
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/S0002-9939-06-08550-9
PII:
S 0002-9939(06)08550-9
Keywords:
Discrete Schr\"odinger operators,
bound states,
oscillation theory
Received by editor(s):
September 3, 2005
Received by editor(s) in revised form:
November 9, 2005
Posted:
October 4, 2006
Additional Notes:
This work was supported by the National Science Foundation under Grant No. DMS-0500910 and the Austrian Science Fund (FWF) under Grant No. P17762
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2006,
American Mathematical Society
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