In this paper we study the Bernstein-Schnabl operators associated with a continuous selection of Borel measures on the unit interval. We investigate their approximation properties by presenting several estimates of the rate of convergence in terms of suitable moduli of smoothness. We also study some shape preserving properties as well as the preservation of the convexity. Moreover we show that their iterates converge to a Markov semigroup whose generator is a degenerate second order elliptic differential operator on the unit interval. Qualitative properties of this semigroup are also investigated together with its asymptotic behaviour.

On Bernstein-Schnabl operators on the unit interval

LEONESSA, VITA;
2008-01-01

Abstract

In this paper we study the Bernstein-Schnabl operators associated with a continuous selection of Borel measures on the unit interval. We investigate their approximation properties by presenting several estimates of the rate of convergence in terms of suitable moduli of smoothness. We also study some shape preserving properties as well as the preservation of the convexity. Moreover we show that their iterates converge to a Markov semigroup whose generator is a degenerate second order elliptic differential operator on the unit interval. Qualitative properties of this semigroup are also investigated together with its asymptotic behaviour.
2008
File in questo prodotto:
File Dimensione Formato  
ALR2008.pdf

non disponibili

Tipologia: Documento in Post-print
Licenza: DRM non definito
Dimensione 225.5 kB
Formato Adobe PDF
225.5 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11563/5066
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 24
  • ???jsp.display-item.citation.isi??? 18
social impact