2022/08/17 by Ana Maria Acu, Acu, Ana-Maria, Margareta Heilmann +5
Mathematics · #41A36 #60E05 #60E10 #Approximation Theory and Sequence Spaces #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical functions and polynomials #Numerical Analysis (math.NA) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2208.08326
openalex publication_date 2022/08/17 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
The idea behind Poisson approximation to the binomial distribution was used in [J. de la Cal, F. Luquin, J. Approx. Theory, 68(3), 1992, 322-329] and subsequent papers in order to establish the convergence of suitable sequences of positive linear operators. The proofs in these papers are given using probabilistic methods. We use similar methods, but in analytic terms. In this way we recover some known results and establish several new ones. In particular, we enlarge the list of the limit operators and give characterizations of them.