Proc. Amer. Math. Soc. 124, 1831-1840 (1996) [DOI: 10.1090/S0002-9939-96-03299-6]

On the Double Commutation Method

Fritz Gesztesy and Gerald Teschl

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).

MSC91: Primary 34B24, 34L05; Secondary 34B20, 47A10
Keywords: Commutation methods, Sturm-Liouville operators, eigenvalues

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