Geodesic
On semigroups with an infinitesimal operator
Jolanta Olko1
1 Institute of Mathematics Pedagogical University Podchor/a/zych 2 30-084 Kraków, Poland
Annales Polonici Mathematici, Tome 85 (2005) no. 1, pp. 77-89

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $\{F^{t}:t\geq 0\}$ be an iteration semigroup of linear continuous set-valued functions. If the semigroup has an infinitesimal operator then it is a uniformly continuous semigroup majorized by an exponential semigroup. Moreover, for sufficiently small $t$ every linear selection of $F^{t}$ is invertible and there exists an exponential semigroup $\{f^{t}:t\geq 0\}$ of linear continuous selections $f^{t}$ of $F^{t}$.
DOI : 10.4064/ap85-1-6
Keywords: geq iteration semigroup linear continuous set valued functions semigroup has infinitesimal operator uniformly continuous semigroup majorized exponential semigroup moreover sufficiently small every linear selection invertible there exists exponential semigroup geq linear continuous selections

Jolanta Olko 1

1 Institute of Mathematics Pedagogical University Podchor/a/zych 2 30-084 Kraków, Poland 
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Jolanta Olko. On semigroups with an infinitesimal operator. Annales Polonici Mathematici, Tome 85 (2005) no. 1, pp. 77-89. doi: 10.4064/ap85-1-6

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