Inverse square singularities and eigenparameter-dependent boundary conditions are two sides of the same coin
نویسندگان
چکیده
Abstract We show that inverse square singularities can be treated as boundary conditions containing rational Herglotz–Nevanlinna functions of the eigenvalue parameter with ‘a negative number poles’. More precisely, we treat in a unified manner one-dimensional Schrödinger operators either an singularity or condition function at each endpoint and define Darboux-type transformations between such operators. These allow one, particular, to transfer almost any spectral result from value problems eigenparameter-dependent those vice versa.
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ژورنال
عنوان ژورنال: Quarterly Journal of Mathematics
سال: 2023
ISSN: ['0033-5606', '1464-3847']
DOI: https://doi.org/10.1093/qmath/haad004