In this paper we introduce a sequence (Mn)nn0 of positive linear operators as a modification of the Bernstein-Schnabl operators associated with a positive projection on C(K), where K is a convex compact subset of a locally convex space; moreover we study its main approximation and qualitative properties. Furthermore, we establish an asymptotic formula for those operators, and we prove that to the sequence (Mn)nn0 there corresponds a uniquely determined C0-semigroup (in some special case a Feller one) which is representable as a limit of suitable powers of the operators.

Modified Bernstein-Schnabl operators on convex compact subsets of locally convex spaces and their limit semigroups / CAPPELLETTI MONTANO M; DIOMEDE S. - In: COMMUNICATIONS IN APPLIED ANALYSIS. - ISSN 1083-2564. - 13 (4):(4)(2009), pp. 609-632.

Modified Bernstein-Schnabl operators on convex compact subsets of locally convex spaces and their limit semigroups

CAPPELLETTI MONTANO, MIRELLA;DIOMEDE, Sabrina
2009

Abstract

In this paper we introduce a sequence (Mn)nn0 of positive linear operators as a modification of the Bernstein-Schnabl operators associated with a positive projection on C(K), where K is a convex compact subset of a locally convex space; moreover we study its main approximation and qualitative properties. Furthermore, we establish an asymptotic formula for those operators, and we prove that to the sequence (Mn)nn0 there corresponds a uniquely determined C0-semigroup (in some special case a Feller one) which is representable as a limit of suitable powers of the operators.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/132030
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