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

   

 

Deforming the point spectra
of one-dimensional Dirac operators


Author: Gerald Teschl
Journal: Proc. Amer. Math. Soc. 126 (1998), 2873-2881
MSC (1991): Primary 34L40, 34L05; Secondary 34B05, 47B25
MathSciNet review: 1451831
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Abstract | References | Similar Articles | Additional Information

Abstract: We provide a method of inserting and removing any finite number of prescribed eigenvalues into spectral gaps of a given one-dimensional Dirac operator. This is done in such a way that the original and deformed operators are unitarily equivalent when restricted to the complement of the subspace spanned by the newly inserted eigenvalue. Moreover, the unitary transformation operator which links the original operator to its deformed version is explicitly determined.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04362-7
PII: S 0002-9939(98)04362-7
Keywords: Spectral theory, Dirac operators, eigenvalues
Received by editor(s): February 18, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 by the author



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