Spectral Theory of Herglotz Functions and Their Compositions

Recent developments in the theory of value distribution for boundary values of Herglotz functions 5], with applications to the spectral analysis of Herglotz measures and differential operators 2, 3] lead in a natural way to the investigation of measures which relate (through the Herglotz representation theorem) to the composition of a pair of Herglotz functions F,G. The present paper provides results on the boundary values of composed Herglotz functions and on the terms of their Herglotz representation which are dominant at large |z|.