Asymptotic formulae for positive linear operators: direct and converse results

Francesco Altomare ^[1] ; Sabrina Diomede ^[1]
1. [1] University of Bari Aldo Moro
  
  University of Bari Aldo Moro
  
  Bari, Italia
Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 2, Nº. 2, 2010, págs. 255-287
Idioma: inglés
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Resumen
- This paper is concerned with asymptotic formulae for sequences of positive linear operators acting on weighted spaces of continuous functions defined on a real interval. The main result provides a characterization of those continuous functions for which a pointwise asymptotic formula holds true. The method is essentially based on a characterization of the domains of generators of C0-semigroups in terms of asymptotic formulae. Finally, several applications concerning, among others, Kantorovich operators, exponential operators, Gauss-Weierstrass operators and a sequence of operators related to the Black-Scholes equation are discussed as well.