.../h/h046/h046320/h0463206.png" /> is the normalized Lebesgue measure on the
circle <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/l
...046/h046320/h046320134.png" /> are defined by the condition (*), where the
circle <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/l
37 KB (5,073 words) - 18:20, 1 December 2014
At points of the unit circle $ | z | = 1 $
3 KB (470 words) - 08:17, 26 March 2023
the convergence also extends over the unit circle if $ \mathop{\rm Re} ( \alpha + \beta - \gamma ) < 0 $;
it converges at all points of the unit circle except $ z = 1 $.
12 KB (1,576 words) - 01:14, 21 January 2022
onto the unit disc $ | \zeta | \leq 1 $
there is a one-to-one correspondence between the points of the circle and the prime ends of $ B $,
5 KB (847 words) - 22:16, 5 June 2020
...op"> L. Carleson, "Sets of uniqueness for functions regular in the unit circle" ''Acta Math.'' , '''87''' : 3–4 (1952) pp. 325–345</TD></TR><TR><T
3 KB (458 words) - 10:23, 2 June 2020
to be normal in the unit disc $ G = \{ {z \in \mathbf C } : {| z | < 1 } \} $
in the unit disc $ G $
7 KB (1,050 words) - 08:03, 6 June 2020
having equal multiplicity. Roots of unit modulus have even multiplicity. It follows that $ w ( z ) = c \prod _ {1}
on the unit circle $ \partial D = \{ {e ^ {it } } : {0 \leq t < 2 \pi } \} $.
9 KB (1,334 words) - 13:15, 26 March 2023
Let $\Delta$ be the open unit disc in the complex plane $\mathbf{C}$, and let $\operatorname{Hol}( \Delta
For $\omega$ on the unit circle $\partial \Delta$, the boundary of $\Delta$, and $\alpha > 1$, a non-tangen
14 KB (2,118 words) - 16:09, 11 February 2024
A circle of unit radius with diametrically-opposite points identified in the Euclidean plane
...elliptic plane is homeomorphic to the real projective plane). A sphere of unit radius with antipoles identified in three-dimensional Euclidean space can s
19 KB (3,123 words) - 23:52, 14 December 2020
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