...orm, weighted class, space with a weight, space of functions with weighted norm''
...ces consisting of functions with infinite ordinary non-weighted norm (semi-norm). Consider, for example, the weighted space $ C _ \phi ( E) $(
9 KB (1,435 words) - 08:13, 13 January 2024
...$K\to K$ that takes $x\in K$ to $\a x$. The element $\N(\a)$ is called the norm of the element $\a$.
...rphism of the multiplicative groups $K^*\to k^*$, which is also called the norm map. For any $\a\in k$,
2 KB (317 words) - 08:59, 15 April 2012
is the norm (semi-norm) of the element $ x $
is the norm (semi-norm) of the element $ x $
2 KB (292 words) - 22:11, 5 June 2020
The $L^p$ norm of $f$ for $1\le p < \infty$ is
For $0 < p < 1$, the $L^p$ norm does not satisfy the triangle inequality.[[#References|[1]]]
1 KB (217 words) - 14:53, 11 November 2023
...or lattice that is at the same time a [[Banach space|Banach space]] with a
norm which satisfies the monotonicity condition:
...ces (cf. [[Orlicz space|Orlicz space]]). In Banach lattices convergence in
norm is (<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.o
9 KB (1,326 words) - 17:14, 7 February 2011
is known as the sharp norm of the form $ \omega $.
i.e. the [[Sharp norm|sharp norm]] of $ X $;
4 KB (552 words) - 16:26, 22 February 2021
''norm residue, Hilbert symbol''
The norm residue of
4 KB (683 words) - 21:24, 11 November 2011
$#C+1 = 107 : ~/encyclopedia/old_files/data/N067/N.0607840 Nuclear norm,
''trace norm''
8 KB (1,266 words) - 08:03, 6 June 2020
$#C+1 = 86 : ~/encyclopedia/old_files/data/S084/S.0804820 Sharp norm
The largest semi-norm $ {| \cdot | } ^ \prime $
5 KB (743 words) - 07:47, 13 May 2022
cf. [[Semi-norm|Semi-norm]]). This topology is locally convex if and only if $ \cup \mathfrak M $
3 KB (419 words) - 08:24, 6 June 2020
$#C+1 = 101 : ~/encyclopedia/old_files/data/N067/N.0607360 Norm on a field
The norm of $ x $
6 KB (1,003 words) - 21:35, 13 January 2021
''t-norm''
If $T$ is a triangular norm, then its ''dual triangular co-norm'' $S$ is given by
6 KB (955 words) - 19:13, 24 November 2023
The number $\lVert x\rVert$ is called the norm of the element $x$.
A vector space $X$ with a distinguished norm is called a [[normed space]]. A norm induces on $X$ a [[metric]] by the formula $dist(x,y)=\lVert x-y\rVert$, he
8 KB (1,284 words) - 21:49, 6 June 2016
...} \mathfrak { P }$ for $x \in L$ integral. Here, $N ( \mathfrak{p} )$, the norm of $\mathfrak{p}$, is the number of elements of the residue field $A _ { K
with $N _ { A } ( x )$ the number of prime ideals in $P _ { A }$ with norm $\leq x$.
3 KB (449 words) - 17:00, 1 July 2020
...nts, de cercles et de sphères dans le plan et dans l'espace" ''Ann. Ecole Norm. Sup.'' , '''1''' (1872) pp. 323–392 {{ZBL|04.0383.01}}</TD></TR>
4 KB (597 words) - 18:10, 1 June 2023
\newcommand{\norm}[1]{\lVert #1\rVert}
The norm of a function $f\in W^l_p(\Omega)$ is given by
8 KB (1,334 words) - 17:47, 30 November 2012
a unique norm such that the completion of $ A \otimes B $
with respect to this norm is a $ C ^ {*} $-
4 KB (651 words) - 15:30, 1 July 2020
can be given by means of a $ p $-homogeneous [[Norm|norm]], $ 0 < p \leq 1 $,
of semi-norms (cf. [[Semi-norm|Semi-norm]]) satisfying
7 KB (1,026 words) - 09:21, 13 May 2022
[[Banach space|Banach space]] with respect to the norm $\|f\|$ and the
[[Pre-norm|pre-norm]] on a vector space $E$ and if $f_0$ is a linear
5 KB (903 words) - 21:31, 3 January 2021
The right-hand side of the Friedrichs inequality gives an equivalent norm in $ W _ {2} ^ {1} ( \Omega ) $.
Using another equivalent norm in $ W _ {2} ^ {1} ( \Omega ) $,
6 KB (825 words) - 19:40, 5 June 2020