Altomare, Francesco:
Asymptotic Formulae for Bernstein-Schnabl Operators and Smoothness
Bollettino dell'Unione Matematica Italiana Serie 9 2 (2009), fasc. n.1, p. 135-150, (English)
pdf (280 Kb), djvu (148 Kb). | MR 2493648 | Zbl 1181.41033
Sunto
Of concern are Bernstein-Schnabl operators associated with a continuous selection of Borel measures on the unit interval. With respect to these sequences of positive linear operators we determine the classes of all continuous functions verifying a pointwise asymptotic formula or a uniform one. Our methods are essentially based on a general characterization of the domains of Feller semigroups in terms of asymptotic formulae and on the determination of both the saturation class of Bernstein-Schnabl operators and the Favard class of the relevant Feller semigroup.
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