denotes the closed unit disc and $ A ( D ) $
the unit circle) such that $ | {f ( t ) } | = \| f \| _ \infty $.
8 KB (1,167 words) - 11:37, 12 January 2021
self-adjoint) operator is symmetric with respect to the unit circle (real line), all elementary divisors corresponding to eigen values $ \lam
...the upper (lower) half-plane is replaced by the exterior (interior) of the unit disc is also valid for $ J $-
9 KB (1,299 words) - 08:07, 6 June 2020
and, in particular, by the unit circle.
...is the theorem of Fatou (1906): If an analytic function is bounded in the unit disc $ D = \{ {z } : {| z | < 1 } \} $,
25 KB (3,676 words) - 08:39, 26 March 2023
...$A ( \mathbf{D} )$ is a typical example of a Dirichlet algebra on the unit circle $\partial \mathbf{D}$. For $A ( \mathbf{D} )$, the measure
7 KB (1,114 words) - 19:36, 23 December 2023
...gle is the length of the arc cut out by the sides of the angle on the unit circle. One radian is assigned to the angle the arc of which has length equal to t
6 KB (1,009 words) - 11:05, 4 December 2016
...contractive operator $T$ in $D$, together with the complement in the unit circle of the union of the arcs along which $m _ { T } ( \lambda )$ can be analyti
6 KB (897 words) - 20:02, 27 February 2021
...and only if there exists a function $\phi \in L ^ { \infty }$ on the unit circle $\bf T$ such that
...t{o}$ and $\text{o}$ is a [[Conformal mapping|conformal mapping]] from the unit disc onto the upper half-plane.
14 KB (2,017 words) - 06:44, 15 February 2024
...ons of the space $\mathbb{R}^3$ around the origin and also to the space of unit tangent vectors to the sphere $S^2$; 4) all compact zero-dimensional groups
...of them (compactness, connectedness, etc.; e.g., a segment differs from a circle in that it can be divided into two by one point); the method of invariants
11 KB (1,634 words) - 17:03, 23 March 2023
...connection between the boundary properties of an analytic function in the unit disc and the metric of the Riemann surface onto which it maps the disc (see
be any domain inside the unit disc $ D= \{ {z } : {| z | < 1 } \} $
7 KB (1,075 words) - 19:29, 1 January 2021
...ction|Generating function]]) appeared as the source of the [[Circle method|circle method]] of Hardy–Littlewood–Ramanujan and the method of trigonometric
...raightedge and a compass (cf. [[Quadrature of the circle|Quadrature of the circle]]) led to questions about the arithmetic nature of the number $ \pi $,
10 KB (1,503 words) - 08:03, 6 June 2020
...g]] of a triangle bounded by arcs of circles onto the upper half-plane (or unit disc) that remains single-valued under unrestricted [[Analytic continuation
...warz functions are automorphic functions with a continuous singular curve (circle or straight line). In particular, the cases of $ \nu _ {1} = 2 $,
5 KB (568 words) - 08:12, 6 June 2020
...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 (1,253 words) - 06:59, 21 July 2024
...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