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Proceedings of the American Mathematical Society

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On the double commutation method


Authors: F. Gesztesy and G. Teschl
Journal: Proc. Amer. Math. Soc. 124 (1996), 1831-1840
MSC (1991): Primary 34B24, 34L05; Secondary 34B20, 47A10
MathSciNet review: 1322925
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Abstract: We provide a complete spectral characterization of the double commutation method for general Sturm-Liouville operators which inserts any finite number of prescribed eigenvalues into spectral gaps of a given background operator. Moreover, we explicitly determine the transformation operator which links the background operator to its doubly commuted version (resulting in extensions and considerably simplified proofs of spectral results even for the special case of Schrödinger-type operators).


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Additional Information

F. Gesztesy
Affiliation: Department of Mathematics, University of Missouri, Colum-bia, Missouri 65211
Email: mathfg@mizzou1.missouri.edu

G. Teschl
Affiliation: Department of Theoretical Physics, Technical University of Graz, Graz, 8010, Austria
Address at time of publication: Institut für Reine und Angewandte Mathematik, Rheinisch-Westfälische Technische Hochschule Aachen, D-52056 Aachen, Germany
Email: mathgr42@mizzou1.missouri.edu, teschl@iram.rwth-aachen.de

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03299-6
Keywords: Commutation methods, Sturm-Liouville operators, eigenvalues
Received by editor(s): December 8, 1994
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society