We study the Bernstein-Schnabl operators associated with a continuous selection of probability Borel measure on a noncompact real interval in the framework of weighted spaces of continuous functions. We investigate their approximation properties and, in addition, we prove that their iterates converge to a positive C_0-semigroup whose generator is a differential operator of the form Au := αu′′. A converse problem on the half line is also discussed.

Bernstein-Schnabl operators on noncompact real intervals

LEONESSA, VITA;
2009-01-01

Abstract

We study the Bernstein-Schnabl operators associated with a continuous selection of probability Borel measure on a noncompact real interval in the framework of weighted spaces of continuous functions. We investigate their approximation properties and, in addition, we prove that their iterates converge to a positive C_0-semigroup whose generator is a differential operator of the form Au := αu′′. A converse problem on the half line is also discussed.
2009
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11563/5068
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