A paper by the leading research fellow at the department of Functional Analysis of the Institute of Mathematics and Mechanics, Namig Guliyev has been published in “The Quarterly Journal of Mathematics” issued by Oxford University Press.

In the paper entitled “Inverse square singularities and eigenparameter dependent boundary conditions are two sides of the same coin” the author shows that inverse square singularities can be treated as boundary conditions containing rational Herglotz–Nevanlinna functions of the eigenvalue parameter with “a negative number of poles”. More precisely, he treats in a unified manner one-dimensional Schrödinger operators with either an inverse square singularity or a boundary condition containing a rational Herglotz–Nevanlinna function of the eigenvalue parameter at each endpoint, and defines Darboux-type transformations between such problems. These transformations allow one, in particular, to transfer almost any spectral result from problems with eigenparameter dependent boundary conditions to those with inverse square singularities, and vice versa.

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