Some analytic properties of semigroups of positive matrices, transition matrices, p-functions and semi-p-functions
Gordon J. Ezekiel · Memorial University Research Repository (Memorial University) · 1983
In this dissertation we deal with four related mathematical entities: transition matrices and their generalization (semigroups of positive matrices), p-functions (which can arise from the diagonal elements of a transition matrix) and their generalization (semi-p-functions). In Chapter 1 we define these entities. In Chapter 2 we discuss continuity under the assumption of measurability alone. The remaining three chapters deal with standard entities only (i.e., those which enjoy a continuity condition at t=0) since most authors assume standardness anyway. Chapter 3 deals with continuity, Chapter 4 with differentiability at t=0, and Chapter 5 with differentiability at t>0. Counter examples are given for outstanding cases.