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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A trace formula and Schmincke inequality on the half-line


Authors: Amin Boumenir and Vu Kim Tuan
Journal: Proc. Amer. Math. Soc. 137 (2009), 1039-1049
MSC (2000): Primary 34L15, 34A55
Published electronically: September 25, 2008
MathSciNet review: 2457445
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Abstract: In this paper we derive a trace formula for the Schrödinger operator on the half-line. As a consequence we obtain a Schmincke type inequality with sharp constant. The main tool in our investigation is the inverse spectral Gelfand-Levitan theory, which allows us to compare two Schrödinger operators whose spectra differ by few eigenvalues.


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Additional Information

Amin Boumenir
Affiliation: Department of Mathematics, University of West Georgia, Carrollton, Georgia 30118
Email: boumenir@westga.edu

Vu Kim Tuan
Affiliation: Department of Mathematics, University of West Georgia, Carrollton, Georgia 30118
Email: vu@westga.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09659-7
PII: S 0002-9939(08)09659-7
Keywords: Trace formula, negative eigenvalues, Schmincke inequality, inverse spectral theory
Received by editor(s): March 31, 2008
Published electronically: September 25, 2008
Communicated by: Walter Craig
Article copyright: © Copyright 2008 American Mathematical Society