Haar space

English

Etymology

Named after Hungarian mathematician Alfréd Haar.

Noun

Haar space (plural Haar spaces)

1. (approximation theory) 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.

   Synonym: Chebyshev space