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Joint subnormality of n-tuples and C₀-semigroups of composition operators on L²-spaces

Piotr Budzyński, Jan Stochel (2007)

Studia Mathematica

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)...

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