Haar space

In approximation theory, a Haar space or Chebyshev space is a finite-dimensional subspace $V$ of $\mathcal C(X, \mathbb K)$ , where $X$ is a compact space and $\mathbb K$ either the real numbers or the complex numbers, such that for any given $f \in \mathcal C(X, \mathbb K)$ there is exactly one element of $V$ that approximates $f$ "best", i.e. with minimum distance to $f$ in supremum norm.

References

{{cite book |last=Shapiro |first=Harold |year=1971 |chapter=2. Best uniform approximation |chapter-url=https://link.springer.com/chapter/10.1007/BFb0058978 |doi=10.1007/BFb0058978 |title=Topics in Approximation Theory |series=Lecture Notes in Mathematics |volume=187 |publisher=Springer |pages=19–22 |isbn=3-540-05376-X}}

Category:Approximation theory