Joint subnormality of a family of composition operators on L²-space is characterized by means of positive definiteness of appropriate Radon-Nikodym derivatives. Next, simplified positive definiteness conditions guaranteeing joint subnormality of a C₀-semigroup of composition operators are supplied. Finally, the Radon-Nikodym derivatives associated to a jointly subnormal C₀-semigroup of composition operators are shown to be the Laplace transforms of probability measures (modulo a C₀-group of scalars) constituting a measurable family.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-2-4,
author = {Piotr Budzy\'nski and Jan Stochel},
title = {Joint subnormality of n-tuples and C0-semigroups of composition operators on L2-spaces},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {167-184},
zbl = {1115.47019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-2-4}
}
Piotr Budzyński; Jan Stochel. Joint subnormality of n-tuples and C₀-semigroups of composition operators on L²-spaces. Studia Mathematica, Tome 178 (2007) pp. 167-184. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm179-2-4/