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Inverse square singularities and eigenparameter-dependent boundary conditions are two sides of the same coin

Inverse square singularities and eigenparameter-dependent boundary conditions are two sides of the same coin

Abstract We show that inverse square singularities can be treated as boundary conditions containing rational Herglotzā€“Nevanlinna functions of the eigenvalue parameter with ā€˜a negative number of polesā€™. More precisely, we treat in a unified manner one-dimensional Schrƶdinger operators with either an inverse square singularity or a boundary condition containing a ā€¦