...cative linear functional has norm 1, each such a functional belongs to the unit sphere of the dual of $ A $.
is closed in the weak topology on the dual space. Since the unit ball is compact in the weak topology on the dual space, $ \Phi $
18 KB (2,806 words) - 03:47, 25 February 2022
...Circular arcs (and diameters) in $E$ which are orthogonal to the boundary circle $\Omega=\{z\colon|z|=1\}$ are called hyperbolic lines. Every point of $\Ome
5 KB (705 words) - 19:16, 14 August 2014
...mbrane is circular. In other words, among all membranes of given area, the circle has the lowest fundamental frequency. This inequality was conjectured by Lo
...i ^ { n / 2 } / \Gamma ( n / 2 + 1 )$ is the volume of the $n$-dimensional unit ball. Equality is attained in (a5) if and only if $\Omega$ is a ball.
13 KB (1,910 words) - 18:40, 19 February 2024
is the unit disc. Then $ G $
be a Fuchsian group acting on the unit disc $ D $.
8 KB (1,210 words) - 10:58, 29 May 2020
has a unit which is the $ \delta $-
of zeros and ones is the Fourier–Stieltjes transform of some measure on the circle if and only if $ (c _ {m} ) $
4 KB (655 words) - 13:07, 7 April 2023
...ubdomain of $B ( 0,1 ) \subseteq \mathbf C$, bounded by an arc of the unit circle and a smooth simple curve $\Gamma \subseteq B ( 0,1 )$ and assume that $f \
...2]]] for references) in the bounded "version" of $H ^ { n }$, namely the unit ball $B$ of $\mathbf{C} ^ { n + 1}$, or, more generally, for bounded domai
6 KB (961 words) - 16:45, 1 July 2020
...rnel]] and as the [[Cauchy kernel|Cauchy kernel]]. In the case of the unit circle, there exists a simple relationship between these kernels:
5 KB (696 words) - 22:17, 28 January 2020
and the selected scale unit $ e $,
...of the number of solutions of the set of equations of the line and of the circle.
8 KB (1,255 words) - 18:47, 5 April 2020
...n over all $H \in H ^ { 2 } ( \mu , {\bf D} )$ ($\mathbf D$ being the open unit disc) satisfying $H ( 0 ) = 1$. If $H$ is restricted to be a polynomial of
...Carathéodory or positive real function because it is analytic in the open unit disc and has positive real part there.
7 KB (1,105 words) - 10:02, 11 November 2023
...464201.png" /> be a complex-valued square-summable function on a
circle of
unit length (or on the segment <img align="absmiddle" border="0" src="https://ww
...al form for results of classical harmonic analysis on the real line or the
circle, but also establishes new results regarding larger classes of topological g
66 KB (9,085 words) - 17:28, 31 March 2020
is the unit circle and $ f _ {i} : S _ {i} \rightarrow S _ {i-} 1 $
4 KB (631 words) - 08:14, 6 June 2020
...polynomials asks how large the values a polynomial must be on the [[unit circle]] in the [[complex plane]] when the coefficients of the polynomial are all
4 KB (641 words) - 08:31, 23 November 2023
algebra is said to be an algebra with a unit if $A$ contains an element $e$ such that $ex=xe=x$ for any
$x\in A$. If a Banach algebra has no unit, a unit may be adjoined, i.e. it is possible to construct a
14 KB (2,346 words) - 22:48, 29 November 2014
...0$ and the roots of $P ( x )$ other than $\theta$ all lie in the open unit circle $| x | < 1$. The set of these numbers is traditionally denoted by $S$. Ever
5 KB (723 words) - 19:03, 23 January 2024
which is homeomorphic to the circle $ S ^ {1} $(
the unit sphere in the Euclidean space $ \mathbf R ^ {3} $).
6 KB (797 words) - 22:12, 5 June 2020
is the parameter on the unit circle $ S ^ {1} $,
...d, D.B. Fuks, "The cohomology of the Lie algebra of vector fields in a circle" ''Funct. Anal. Appl.'' , '''2''' (1968) pp. 342–343 ''Funkts. Anal.
10 KB (1,539 words) - 11:16, 23 March 2023
...s in the upper half-plane, and that of a unitary operator lies on the unit circle). If the scalar product is not of fixed sign, but its index of indefinitene
points outside the unit circle. For $ J $-
16 KB (2,424 words) - 08:22, 6 June 2020
...logarithmic Mahler measure $m ( P )$ is defined to be the average over the unit $n$-torus of $\operatorname { log } | P ( x _ { 1 } , \dots , x _ { n } ) |
...lign="top"> C.J. Smyth, "On the product of the conjugates outside the unit circle of an algebraic integer" ''Bull. London Math. Soc.'' , '''3''' (1971) pp. 1
7 KB (1,101 words) - 14:50, 27 January 2024
...refers to representations of an invertible matrix-function $f$ on the unit circle $\mathcal{T}$ of the form $f = f_+ . \delta . f_-$, where $f _ { \pm }$ are
...standard decomposition of the Riemann sphere $S$, where $D _ { + }$ is the unit disc and $D_{-}$ is the complementary domain containing the point $\{ \inft
7 KB (989 words) - 16:56, 1 July 2020
...ecial case of a normal operator, the spectral measure is given on the unit circle. The spectral decomposition of a unitary operator $ U $
5 KB (793 words) - 08:22, 6 June 2020