Haar space

Noun

Meaning

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

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