Geodesic
Asymptotic Formulae for Bernstein-Schnabl Operators and Smoothness
Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 1, pp. 135-150.

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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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Altomare, Francesco. Asymptotic Formulae for Bernstein-Schnabl Operators and Smoothness. Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 1, pp. 135-150. http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_1_a6/

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