Extension of Bernstein Polynomials to Infinite Dimensional Case
Functional Analysis
2010-05-27 v1 Classical Analysis and ODEs
Abstract
The purpose of this paper is to study some new concrete approximation processes for continuous vector-valued mappings defined on the infinite dimensional cube or on a subset of a real Hilbert space. In both cases these operators are modelled on classical Bernstein polynomials and represent a possible extension to an infinite dimensional setting. The same idea is generalized to obtain from a given approximation process for function defined on a real interval a new approximation process for vector-valued mappings defined on subsets of a real Hilbert space.
Cite
@article{arxiv.math/0603186,
title = {Extension of Bernstein Polynomials to Infinite Dimensional Case},
author = {Lorenzo D'Ambrosio},
journal= {arXiv preprint arXiv:math/0603186},
year = {2010}
}
Comments
14 pages. to appear on Journal of Approximation Theory