Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Renormalized oscillation theory
for Dirac operators


Author: Gerald Teschl
Journal: Proc. Amer. Math. Soc. 126 (1998), 1685-1695
MSC (1991): Primary 34C10, 39L40; Secondary 34B24, 34L15
MathSciNet review: 1443411
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Oscillation theory for one-dimensional Dirac operators with separated boundary conditions is investigated. Our main theorem reads: If $\lambda _{0,1}\in \mathbb R$ and if $u,v$ solve the Dirac equation $H u= \lambda _0 u$, $H v= \lambda _1 v$ (in the weak sense) and respectively satisfy the boundary condition on the left/right, then the dimension of the spectral projection $P_{(\lambda _0, \lambda _1)}(H)$ equals the number of zeros of the Wronskian of $u$ and $v$. As an application we establish finiteness of the number of eigenvalues in essential spectral gaps of perturbed periodic Dirac operators.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 34C10, 39L40, 34B24, 34L15

Retrieve articles in all journals with MSC (1991): 34C10, 39L40, 34B24, 34L15


Additional Information

Gerald Teschl
Affiliation: Institut für Reine und Angewandte Mathematik RWTH Aachen 52056 Aachen Germany
Address at time of publication: Institut für Mathematik, Universität Wien, Strudelhofgasse 4, 1090 Vienna, Austria
Email: gerald@mat.univie.ac.at

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04310-X
PII: S 0002-9939(98)04310-X
Keywords: Oscillation theory, Dirac operators, spectral theory
Received by editor(s): November 7, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 by the author