A remark on the discriminant of Hill's equation and Herglotz functions

Abstract

We establish a link between the basic properties of the discriminant of periodic second-order differential equations and an elementary analysis of Herglotz functions. Some generalizations are presented using the language of self-adjoint extensions.

5 pages. This is preliminary version. The final version is accepted in Archiv der Mathematik (Basel) published by Birkhaeuser

References in corpus (3)

• Spectra of self-adjoint extensions and applications to solvable Schroedinger operators
• Large gaps in point-coupled periodic systems of manifolds
• Unitary dimension reduction for a class of self-adjoint extensions with applications to graph-like structures