On the double commutation method

Gesztesy, F.; Teschl, G.

doi:10.1090/S0002-9939-96-03299-6

On the double commutation method
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by F. Gesztesy and G. Teschl PDF

Proc. Amer. Math. Soc. 124 (1996), 1831-1840 Request permission

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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