Abstract

Deepening the study of a new approximation sequence of positive linear operators we introduced and studied in [10], in this paper we disclose its relationship with the Markov semigroup (pre)generation problem for a class of degenerate second-order elliptic dierential operators which naturally arise through an asymptotic formula, as well as with the approximation of the relevant Markov semigroups in terms of the approximating operators themselves. The analysis is carried out in the context of the space C (K) of all continuous functions dened on an arbitrary compact convex subset K of Rd, d 1, having non-empty interior and a not necessarily smooth boundary, as well as, in some particular cases, in Lp(K) spaces, 1 <p < +\infty. The approximation formula also allows to infer some preservation properties of the semigroup such as the preservation of the Lipschitz-continuity as well as of the convexity. We nally apply the main results to some noteworthy particular settings such as balls and ellipsoids, the unit interval and multidimensonal hypercubes and simplices. In these settings the relevant dierential operators fall into the class of Fleming-Viot operators.

Autore Pugliese

• Altomare Francesco , Cappelletti Montano Mirella

Tutti gli autori

• ALTOMARE F.;CAPPELLETTI MONTANO M.

Titolo volume/Rivista

Non Disponibile

Anno di pubblicazione

2018

ISSN

0022-247X

ISBN

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Numero di citazioni Wos

Nessuna citazione

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Numero di citazioni Scopus

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Settori ERC

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Codici ASJC

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