...e unit disc $D = \{ z \in \mathbf{C} : |z| < 1 \}$; then all points of the circle $\Gamma = \{ z \in \mathbf{C} : |z| = 1 \}$ except, possibly, for a [[First
2 KB (313 words) - 19:43, 18 April 2017
...aofmath.org/legacyimages/m/m064/m064430/m06443021.png" /> is an arc of the
circle <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/l
...ar group (1) is then replaced by the modular group of automorphisms of the
unit disc. For example, it is convenient to apply the fractional-linear transfor
39 KB (5,287 words) - 17:07, 7 February 2011
...explains the connection of roots of unity with the problem of squaring the circle (construction of polygons, cf. [[Geometric constructions|Geometric construc
4 KB (680 words) - 13:40, 30 December 2018
of functions of bounded type in the unit disc $ \Delta = \{ {z \in \mathbf C } : {| z | < 1 } \} $:
almost-everywhere on the unit circle $ \Gamma = \{ {z \in \mathbf C } : {| z | = 1 } \} $;
8 KB (1,170 words) - 19:40, 5 June 2020
...(cf. [[Spectrum of an operator|Spectrum of an operator]]) lies on the unit circle, and $U$ has a representation
2 KB (433 words) - 12:44, 18 August 2014
analytic on the open unit disc $ | z | < 1 $(
...s the [[Banach algebra|Banach algebra]] of complex-valued functions on the unit disc having a [[Fourier series|Fourier series]]
6 KB (869 words) - 11:06, 30 May 2020
...opediaofmath.org/legacyimages/b/b110/b110130/b11013061.png" /> on the
unit circle <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/l
...w.encyclopediaofmath.org/legacyimages/b/b110/b110130/b11013075.png" /> and
unit <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/l
41 KB (5,422 words) - 22:26, 1 January 2018
...tionals on $ $ is closed in the weak topology on the dual space. Since the unit ball is compact in the weak topology on the dual space, $ $ is also compact
...number of generators in the algebra $ $, where $ $ is the $ $-dimensional unit sphere, is equal to $ $; a similar result holds for an arbitrary $ $-dimens
14 KB (2,175 words) - 17:06, 16 April 2012
...ametrized by a unit vector $\alpha \in S ^ { 1 }$, $S ^ { 1 }$ is the unit circle in $\mathbf{R} ^ { 2 }$ and $p \in \mathbf R _ { + } : = [ 0 , \infty )$. B
If $n_0$ is a unit vector normal to $S$ at the point $x _ { 0 }$, then for an arbitrary $\gamm
6 KB (922 words) - 14:50, 27 January 2024
Let $a$ be a complex-valued function defined on the complex unit circle $\bf T$, with [[Fourier coefficients|Fourier coefficients]]
...he exponentials of continuous complex-valued functions defined on the unit circle.
13 KB (1,838 words) - 07:22, 13 February 2024
is the unit $ n \times n $
...style="background-color:white;" colspan="1">Situated inside or on the unit circle; in the latter case simple elementary divisors of the monodromy matrix corr
22 KB (3,165 words) - 08:59, 21 January 2024
.../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