Aleksey Kostenko, Alexander Sakhnovich, Gerald Teschl
Commutation Methods for Schrödinger Operators with Strongly Singular Potentials
The paper is published: Math. Nachr. 285 (2012) 392-410

MSC:

34B20 Weyl theory and its generalizations

34L05 General spectral theory

34B24 Sturm-Liouville theory, See also {34Lxx}

47A10 Spectrum, resolvent

Abstract: 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
Schr\"odinger operators (also known as Bessel operators). We also investigate the connections
with the generalized B\"acklund--Darboux transformation.


Keywords: Schrodinger operators, spectral theory, commutation methods, strongly singular potentials
Notes: second and final version