Proceedings of the American Mathematical Society

Author(s): F. Gesztesy; G. Teschl
Journal: Proc. Amer. Math. Soc. 124 (1996), 1831-1840.
MSC (1991): Primary 34B24, 34L05; Secondary 34B20, 47A10
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 34B24, 34L05, 34B20, 47A10

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

G. Teschl
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211 - 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: 10.1090/S0002-9939-96-03299-6
PII: S 0002-9939(96)03299-6
Keywords: Commutation methods, Sturm-Liouville operators, eigenvalues
Received by editor(s): December 8, 1994
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1996, American Mathematical Society

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