Elliptic differential operators and positive semigroups associated with generalized Kantorovich operators

摘要

AbstractDeepening the study of a new approximation sequence of positive linear operators we introduced and studied in , in this paper we disclose its relationship with the Markov semigroup (pre)generation problem for a class of degenerate second-order elliptic differential 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 spaceC(K)of all continuous functions defined on an arbitrary convex compact subsetKofRd,d≥1, having non-empty interior and a not necessarily smooth boundary, as well as, in some particular cases, inLp(K