Joint subnormality of a family of composition operators on $L^2$-space is characterized by means of positive definiteness of appropriate Radon–Nikodym derivatives. Next, simplified positive definiteness conditions guaranteeing joint subnormality of a $C_0$-semigroup of composition operators are supplied. Finally, the Radon–Nikodym derivatives associated to a jointly subnormal $C_0$-semigroup of composition operators are shown to be the Laplace transforms of probability measures (modulo a $C_0$-group of scalars) constituting a measurable family.
Piotr Budzy/nski; Jan Stochel. Joint subnormality of $n$-tuples and
$C_0$-semigroups of composition operators on $L^2$-spaces. Studia Mathematica, Tome 179 (2007) no. 2, pp. 167-184. doi: 10.4064/sm179-2-4
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author = {Piotr Budzy/nski and Jan Stochel},
title = {Joint subnormality of $n$-tuples and
$C_0$-semigroups of composition operators on $L^2$-spaces},
journal = {Studia Mathematica},
pages = {167--184},
year = {2007},
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doi = {10.4064/sm179-2-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm179-2-4/}
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