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.File in questo prodotto:
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