On Hilbert extensions of Weierstrass" theorem with weights
Articles
Overview
published in
- Journal of Function Spaces Journal
publication date
- January 2010
start page
- 201
end page
- 213
issue
- 2
volume
- 8
Digital Object Identifier (DOI)
full text
International Standard Serial Number (ISSN)
- 2314-8896
Electronic International Standard Serial Number (EISSN)
- 2314-8888
abstract
- In this paper we study the set of ℊ-valued functions which can be approximated by ℊ-valued continuous functions in the norm mathematical equation, where I ⊂ ℝ is a compact interval, ℊ is a separable real Hilbert space and w is a certain ℊ-valued weakly measurable weight. Thus, we obtain a new extension of the celebrated Weierstrass approximation theorem.
Classification
subjects
- Mathematics
keywords
- weierstrass theorem; g -valued weights; g -valued polynomials; g -valued continuous functions.