This note discusses the indecomposability and decomposability of certain operators occurring frequently in approximation theory: piecewise linear interpolation and Bernsteintype operators. The second topic includes the central (absolute) moments of the composition of two operators and their asymptotic behavior.
We indicate some qualitative properties of Fleming--Viot second order differential operators on the d-dimensional simplex, such as an inductive characterization of its domain and some spectral properties connected with the
asymptotic behavior of the generated semigroup. These properties turn out to be very useful in the approximation of the solution
of the evolution problem associated with Fleming--Viot operators, which are very important as diffusion models in population
We study the degree of approximation of the iterated Bernstein operators to the members (T(t)) t ≧0, of their limiting semigroup. This yields a full quantitative version of an earlier convergence result by Karlin and Ziegler.
In this paper, we study the k-th order Kantorovich type modication of Szász—Mirakyan operators. We first establish explicit formulas giving the images of monomials and the moments up to order six. Using this modification, we present a quantitative Voronovskaya theorem for differentiated Szász—Mirakyan operators in weighted spaces. The approximation properties such as rate of convergence and simultaneous approximation by the new constructions are also obtained.