Distributional chaos for strongly continuous semigroups is studied and characterized. It is shown to be equivalent to the existence of a distributionally irregular vector. Finally, a sufficient condition for distributional chaos on the point spectrum of the generator of the semigroup is presented. An application to the semigroup generated in $L^2(\mathbb{R})$ by a translation of the Ornstein-Uhlenbeck operator is also given.
Distributional chaos for strongly continuous semigroups of operators
ALBANESE, Angela Anna;MANGINO, Elisabetta Maria;
2013-01-01
Abstract
Distributional chaos for strongly continuous semigroups is studied and characterized. It is shown to be equivalent to the existence of a distributionally irregular vector. Finally, a sufficient condition for distributional chaos on the point spectrum of the generator of the semigroup is presented. An application to the semigroup generated in $L^2(\mathbb{R})$ by a translation of the Ornstein-Uhlenbeck operator is also given.File in questo prodotto:
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