Extension of Bernstein Polynomials to Infinite Dimensional Case

Details Extension of Bernstein Polynomials to Infinite Dimensional Case Extension of Bernstein Polynomials to Infinite Dimensional Case

2006-03-08

arxiv.org/abs/math/0603186v1

Journal of Approximation Theory 140 (2006) 191 - 202

Mathematics

Functional Analysis

14 pages. to appear on Journal of Approximation Theory

Scientific paper

10.1016/j.jat.2005.12.006

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.

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