Haar space
التعريفات والمعاني
== English ==
=== Etymology ===
Named after Hungarian mathematician Alfréd Haar.
=== Noun ===
Haar space (plural Haar spaces)
(approximation theory) A finite-dimensional subspace
V
{\displaystyle V}
of
C
(
X
,
K
)
{\displaystyle {\mathcal {C}}(X,\mathbb {K} )}
, where
X
{\displaystyle X}
is a compact space and
K
{\displaystyle \mathbb {K} }
either the real numbers or the complex numbers, such that for any given
f
∈
C
(
X
,
K
)
{\displaystyle f\in {\mathcal {C}}(X,\mathbb {K} )}
there is exactly one element of
V
{\displaystyle V}
that approximates
f
{\displaystyle f}
"best", i.e. with minimum distance to
f
{\displaystyle f}
in supremum norm.
Synonym: Chebyshev space