English

Approximation processes by multidimensional Bernstein-type exponential polynomials on the hypercube

Classical Analysis and ODEs 2024-05-28 v1 Functional Analysis

Abstract

In this paper we introduce a new family of Bernstein-type exponential polynomials on the hypercube [0,1]d[0, 1]^d and study their approximation properties. Such operators fix a multidimensional version of the exponential function and its square. In particular, we prove uniform convergence, by means of two different approaches, as well as a quantitative estimate of the order of approximation in terms of the modulus of continuity of the approximated function.

Keywords

Cite

@article{arxiv.2405.16935,
  title  = {Approximation processes by multidimensional Bernstein-type exponential polynomials on the hypercube},
  author = {Laura Angeloni and Danilo Costarelli and Chiara Darielli},
  journal= {arXiv preprint arXiv:2405.16935},
  year   = {2024}
}