In mathematical analysis, the uniform norm (or sup norm) assigns, to real- or complex-valued bounded functions ⁠ f {\displaystyle f} ⁠ defined on a set...

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...

}(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...

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...

is a Banach space, pointwise boundedness is equivalent to uniform boundedness in operator norm. The theorem was first published in 1927 by Stefan Banach...

{\displaystyle C(\mathbb {R} )} continuous functions endowed with the uniform norm topology C c ( R ) {\displaystyle C_{c}(\mathbb {R} )} continuous functions...

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...

using polynomials when the merit function is the maximum difference (uniform norm). Its discovery is attributed to Chebyshev. Let f {\displaystyle f} be...

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...

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...

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...

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...

{\displaystyle L^{\infty }} -norm or maximum norm (or uniform norm) is the limit of the L p {\displaystyle L^{p}} -norms for p → ∞ {\displaystyle p\to...

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...

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...

_{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...

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...

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...

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...

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...

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...

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...

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...

(1925) defined the uniformly almost-periodic functions as the closure of the trigonometric polynomials with respect to the uniform norm ‖ f ‖ ∞ = sup x |...

norm on A {\displaystyle A} is the uniform norm (or sup-norm) on X {\displaystyle X} , then A {\displaystyle A} is called a uniform algebra. Uniform algebras...

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...

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...

{R} ^{n};\mathbb {R} )} equipped with the uniform norm, since one can bound the uniform norm with the norm of Θ n + 1 2 ( R n ; R ) {\displaystyle \Theta...

{\displaystyle [-\pi ,\pi ]} with the uniform norm. This is the content of the Weierstrass theorem on the uniform density of trigonometric polynomials...

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...