Value Distribution and Spectral Theory
David B. Pearson · Proceedings of the London Mathematical Society · 1994
We develop the theory of value distribution for the class of functions defined by boundary values of Herglotz functions. Examples include boundary values of resolvents of Hilbert space operators, and boundary values of the m-function for differential operators. Precise expressions are derived for value distribution, and related to spectral properties of the corresponding measures. As special cases, we evaluate | F 0 − 1 ( S ) | where the corresponding measure μ is purely singular or finite, and construct the local probability density for value distribution where μ has an absolutely continuous component.