ON FINITE ABSOLUTE CONTINUITY OF MEASURES RELATED TO WIENER MEASURE

In this paper we study finite absolute continuity with respect to Wiener measure. A general condition of finite absolute continuity in terms of disintegration of measures is given. Finite absolute continuity of Itô processes and conditional distributions of the Wiener process is studied.

DISINTEGRATION-OF-MEASURE TECHNIQUES FOR COMMUTING MULTIVARIABLE WEIGHTED SHIFTS

We employ techniques from the theory of disintegration of measures to study the Lifting Problem for commuting $n$-tuples of subnormal weighted shifts. We obtain a new necessary condition for the existence of a lifting, and generate new pathology associated with bringing together the Berger measures associated to each individual weighted shift. For subnormal $2$-variable weighted shifts, we then find the precise relation between the Berger measure of the pair and the Berger measures of the shifts associated to horizontal rows and vertical columns of weights.