Math. Nachr. 285, 392-410 (2012) [DOI: 10.1002/mana.201000108]

Commutation Methods for Schrödinger Operators with Strongly Singular Potentials

Aleksey Kostenko, Alexander Sakhnovich, and Gerald Teschl

We explore the connections between singular Weyl-Titchmarsh theory and the single and double commutation methods. In particular, we compute the singular Weyl function of the commuted operators in terms of the original operator. We apply the results to spherical Schrödinger operators (also known as Bessel operators). We also investigate the connections with the generalized Bäcklund-Darboux transformation.

MSC2010: Primary 34B20, 34L05; Secondary 34B24, 47A10
Keywords: Schrödinger operators, spectral theory, commutation methods, strongly singular potentials

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