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On semigroups with an infinitesimal operator

100%

Olko J.

Annales Polonici Mathematici

2005

tom 85

nr 1

77-89

Let ${F^{t}: t ≥ 0}$ 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 ${f^{t}:t ≥ 0}$ of linear continuous selections $f^{t}$ of $F^{t}$.

Concave iteration semigroups of linear set-valued functions

100%

Olko J.

Annales Polonici Mathematici

1999

tom 71

nr 1

31-38

We consider a concave iteration semigroup of linear continuous set-valued functions defined on a closed convex cone in a separable Banach space. We prove that such an iteration semigroup has a selection which is also an iteration semigroup of linear continuous functions. Moreover it is majorized by an "exponential" family of linear continuous set-valued functions.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Olko J.

1 2005

1 1999

Wyniki wyszukiwania

On semigroups with an infinitesimal operator

Concave iteration semigroups of linear set-valued functions