Displaying similar documents to “Integrated Semigroups and Integrodifferential Equations.”

Around the Kato generation theorem for semigroups

Jacek Banasiak, Mirosław Lachowicz (2007)

Studia Mathematica

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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.

Frequently hypercyclic semigroups

Elisabetta M. Mangino, Alfredo Peris (2011)

Studia Mathematica

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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...

α-times integrated semigroups: local and global

Miao Li, Quan Zheng (2003)

Studia Mathematica

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We investigate the relations between local α-times integrated semigroups and (α + 1)-times integrated Cauchy problems, and then the relations between global α-times integrated semigroups and regularized semigroups.