In mathematical analysis, the uniform norm (or sup norm) assigns, to real- or complex-valued bounded functions f {\displaystyle f} defined on a set...
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In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance...
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}(A,B)=\|h_{A}-h_{B}\|_{\infty }} where, on the right hand side, the uniform norm on the unit sphere is used. The properties of the support function as...
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bounded real or complex-valued functions over X with the uniform norm topology, with the uniform metric defined by d ( f , g ) = ‖ f − g ‖ ∞ = sup x ∈ X...
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is a Banach space, pointwise boundedness is equivalent to uniform boundedness in operator norm. The theorem was first published in 1927 by Stefan Banach...
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mathematics, in the field of additive combinatorics, a Gowers norm or uniformity norm is a class of norms on functions on a finite group or group-like object which...
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Function space (section Norm)
{\displaystyle C(\mathbb {R} )} continuous functions endowed with the uniform norm topology C c ( R ) {\displaystyle C_{c}(\mathbb {R} )} continuous functions...
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using polynomials when the merit function is the maximum difference (uniform norm). Its discovery is attributed to Chebyshev. Let f {\displaystyle f} be...
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itself a Banach space under the uniform norm. The uniform limit theorem also holds if continuity is replaced by uniform continuity. That is, if X and Y...
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Mathematically, the Chebyshev distance is a metric induced by the supremum norm or uniform norm. It is an example of an injective metric. In two dimensions, i.e...
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a normed space with norm defined by ‖ f ‖ = sup x ∈ X | f ( x ) | , {\displaystyle \|f\|=\sup _{x\in X}|f(x)|,} the uniform norm. The uniform norm defines...
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A social norm is a shared standard of acceptable behavior by a group. Social norms can both be informal understandings that govern the behavior of members...
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Topological tensor product (redirect from Uniform cross norm)
tensor norm is defined to be a finitely generated uniform crossnorm. The projective cross norm π {\displaystyle \pi } and the injective cross norm ε {\displaystyle...
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_{n=0}^{\infty }f_{n}(x)} is called normally convergent if the series of uniform norms of the terms of the series converges, i.e., ∑ n = 0 ∞ ‖ f n ‖ := ∑ n...
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the uniform norm. Namely, for each continuous function φ : I a ( t 0 ) → B b ( y 0 ) , {\displaystyle \varphi :I_{a}(t_{0})\to B_{b}(y_{0}),} the norm of...
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L-infinity (category Normed spaces)
0:|f(x)|\leq C{\text{ for almost every }}x\}.} This norm is the uniform norm, it is an L p {\displaystyle L^{p}} norm for p = ∞ . {\displaystyle p=\infty .} The...
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on a compact Hausdorff space with respect to its uniform norm, then it is bounded in the uniform norm on C(X) and in particular is pointwise bounded. Let...
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Equicontinuity (redirect from Uniform equicontinuity)
separable. Let X be a compact Hausdorff space, and equip C(X) with the uniform norm, thus making C(X) a Banach space, hence a metric space. Then Arzelà–Ascoli...
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value symbols stand for a metric for the space of solutions such as the uniform norm. Similar definitions also apply for non-grid discretization schemes such...
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approximations by functions in a Chebyshev space that are the best in the uniform norm L∞ sense. It is sometimes referred to as Remes algorithm or Reme algorithm...
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0430357} yields the optimal approximation (the best in the sense of the uniform norm of the error). However, this value is not used by the algorithm as it...
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Almost periodic function (redirect from Uniformly almost periodic function)
(1925) defined the uniformly almost-periodic functions as the closure of the trigonometric polynomials with respect to the uniform norm ‖ f ‖ ∞ = sup x |...
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every algebra norm on C(X) is equivalent to the usual uniform norm. (Kaplansky himself had earlier shown that every complete algebra norm on C(X) is equivalent...
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functional analysis, a uniform algebra A on a compact Hausdorff topological space X is a closed (with respect to the uniform norm) subalgebra of the C*-algebra...
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the image of the unit ball is relatively compact in C([a,b]) with the uniform norm and a fortiori in L2[a,b]. Now apply the spectral theorem for compact...
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Inner product space (category Normed spaces)
{\displaystyle [-\pi ,\pi ]} with the uniform norm. This is the content of the Weierstrass theorem on the uniform density of trigonometric polynomials...
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Bounded operator (section In normed vector spaces)
continuous functions on [ a , b ] {\displaystyle [a,b]} endowed with the uniform norm and with values in the space C [ c , d ] {\displaystyle C[c,d]} with...
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Càdlàg (section Generalization of the uniform topology)
E | f ( t ) | {\displaystyle \|f\|:=\sup _{t\in E}|f(t)|} denote the uniform norm on functions on E {\displaystyle E} . Define the Skorokhod metric σ {\displaystyle...
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dense in the space of continuous functions on the unit circle, with the uniform norm; this is a special case of the Stone–Weierstrass theorem. More concretely...
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