On Hilbert extensions of Weierstrass" theorem with weights Articles uri icon

publication date

  • January 2010

start page

  • 201

end page

  • 213

issue

  • 2

volume

  • 8

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.

subjects

  • Mathematics

keywords

  • weierstrass theorem; g -valued weights; g -valued polynomials; g -valued continuous functions.