Hull

The research over the past 10 years by D. Pearson's group has been focussed on developments in spectral theory for the m-function, particularly in relating spectral properties to a general spectral asymptotics for solutions of the equation at real spectral parameter.This work is based on 3 fundamental papers relating to value distribution for boundary values of Herglotz functions, and other results have been obtained which extend the theory of subordinacy in new directions. Current work is leading to a new characterisation of spectral asymptotics applicable to the a.c.spectrum. Recently this has been developed to include the spectral properties of the Schrödinger operators in higher dimensions, us ing ideas borrowed from the Weyl-Titchmarsh theory.