Geometrical aspects of spectral theory and value distribution for Herglotz functions
The authors show how the spectral theory for Herglotz functions and differential operators is related to and dependent on the geometrical properties of the complex upper half-plane, viewed as a hyperbolical space. They next establish the theory of value distribution for real-valued Lebesgue measurable functions \(f\) and introduce the value distribution function associated with any given Herglotz function \(F\). The theory of value distribution for boundary values of Herglotz functions is related to the description of asymptotics for solutions of the Schrödinger equation on the half-line.
scientific article; zbMATH DE number 1908554