Arithmetical semigroups I: direct factors.
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J. KNOPFMACHER, K.-H. Indlekofer, R. Warlimont (1991)
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Franz Halter-Koch, Richard Warlimont (1994)
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Elisabetta M. Mangino, Alfredo Peris (2011)
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We study frequent hypercyclicity in the context of strongly continuous semigroups of operators. More precisely, we give a criterion (sufficient condition) for a semigroup to be frequently hypercyclic, whose formulation depends on the Pettis integral. This criterion can be verified in certain cases in terms of the infinitesimal generator of the semigroup. Applications are given for semigroups generated by Ornstein-Uhlenbeck operators, and especially for translation semigroups on weighted...
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Jacek Banasiak, Mirosław Lachowicz (2007)
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We show that the result of Kato on the existence of a semigroup solving the Kolmogorov system of equations in l₁ can be generalized to a larger class of the so-called Kantorovich-Banach spaces. We also present a number of related generation results that can be proved using positivity methods, as well as some examples.
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