Asymptotic Formulae for Bernstein-Schnabl Operators and Smoothness

Francesco Altomare

Bollettino dell'Unione Matematica Italiana (2009)

  • Volume: 2, Issue: 1, page 135-150
  • ISSN: 0392-4041

Abstract

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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.

How to cite

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Altomare, Francesco. "Asymptotic Formulae for Bernstein-Schnabl Operators and Smoothness." Bollettino dell'Unione Matematica Italiana 2.1 (2009): 135-150. <http://eudml.org/doc/290570>.

@article{Altomare2009,
abstract = {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.},
author = {Altomare, Francesco},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {135-150},
publisher = {Unione Matematica Italiana},
title = {Asymptotic Formulae for Bernstein-Schnabl Operators and Smoothness},
url = {http://eudml.org/doc/290570},
volume = {2},
year = {2009},
}

TY - JOUR
AU - Altomare, Francesco
TI - Asymptotic Formulae for Bernstein-Schnabl Operators and Smoothness
JO - Bollettino dell'Unione Matematica Italiana
DA - 2009/2//
PB - Unione Matematica Italiana
VL - 2
IS - 1
SP - 135
EP - 150
AB - 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.
LA - eng
UR - http://eudml.org/doc/290570
ER -

References

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