A paper by the leading research fellow at the department of Functional Analysis of the Institute of Mathematics and Mechanics, Namig Guliyev, published in The Quarterly Journal of Mathematics issued by Oxford University Press, has been included in the collection of high-impact research from the journal. This collection consists of the most read and most cited articles making an impact in the Quarterly Journal of Mathematics published within the past two years.<\/p>\n
In the paper entitled \u201cInverse square singularities and eigenparameter dependent boundary conditions are two sides of the same coin\u201d the author shows that inverse square singularities can be treated as boundary conditions containing rational Herglotz\u2013Nevanlinna functions of the eigenvalue parameter with \u201ca negative number of poles\u201d. More precisely, he treats in a unified manner one-dimensional Schr\u00f6dinger operators with either an inverse square singularity or a boundary condition containing a rational Herglotz\u2013Nevanlinna 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.<\/p>\n
The collection can be found on the following webpage:<\/p>\n