Decomposition and Quasi-invariance of Vector-valued Analytic Measures
by
Annela Kelly
Northeast Louisiana University

While generalizing the F. and M. Riesz theorem to compact abelian groups, Helson and Lowdenslager concluded that the result does not hold for compact abelian groups, i.e. analytic measure may not be absolutely continuous with respect to Haar measure. However, its absolutely continuous part and singular part are each analytic.

We generalize the result to vector-valued measures. In particular, we show that the absolutely continuous part and the singular part of a weakly analytic vector-valued measure are each weakly analytic. Moreover, we prove that a weakly analytic vector-valued measure is quasi-invariant.

Date received: April 30, 1999