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Czasopisma help

  1. 2 Studia Mathematica

Autorzy help

  1. 2 Budzyński P.

  2. 2 Stochel J.

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  1. 1 2009

  2. 1 2007

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

100%
Budzyński P., Stochel J.
Studia Mathematica
|
2009
|
tom 193
|
nr 1
29-52
EN
In the previous paper, we have characterized (joint) subnormality of a C₀-semigroup of composition operators on L²-space by positive definiteness of the Radon-Nikodym derivatives attached to it at each rational point. In the present paper, we show that in the case of C₀-groups of composition operators on L²-space the positive definiteness requirement can be replaced by a kind of consistency condition which seems to be simpler to work with. It turns out that the consistency condition also characterizes subnormality of C₀-semigroups of composition operators on L²-space induced by injective and bimeasurable transformations. The consistency condition, when formulated in the language of the Laplace transform, takes a multiplicative form. The paper concludes with some examples.
2
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Joint subnormality of n-tuples and C₀-semigroups of composition operators on L²-spaces

100%
Budzyński P., Stochel J.
Studia Mathematica
|
2007
|
tom 179
|
nr 2
167-184
EN
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.
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