is a bounded regular [[Analytic function|analytic function]] in the unit disc $ D = \{ {z \in \mathbf C } : {| z | < 1 } \} $
of the circle $ \Gamma = \{ {z } : {| z | = 1 } \} $
5 KB (791 words) - 08:11, 6 June 2020
of measure zero on the unit circle $ \Gamma = \{ {z } : {| z | = 1 } \} $,
that is regular, analytic and bounded in the unit disc $ D = \{ {z } : {| z | < 1 } \} $
3 KB (354 words) - 04:11, 6 June 2020
...p"> P.E. Blanksby, H.L. Montgomery, "Algebraic integers near the unit circle" ''Acta Arith.'' , '''18''' (1971) pp. 355–369</TD></TR>
7 KB (1,029 words) - 07:50, 27 March 2018
...o, then $f(z)=0$ in $D$. Moreover, there is no meromorphic function in the unit disc that takes infinite radial boundary values on a set $E$ of the given t
3 KB (424 words) - 21:56, 24 July 2012
...mages/c/c026/c026230/c0262306.png" /> rotates only in one direction as the circle is traversed. The following inequality expresses a necessary and sufficient
....org/legacyimages/c/c026/c026230/c02623054.png" />, and the radius of this circle cannot be increased without imposing additional restrictions on the class o
19 KB (2,650 words) - 17:07, 7 February 2011
...nction $u(z)$, $z=r\mathrm{e}^{\mathrm{i}\phi}$, can be represented in the unit disc $U=\{ z\in\C : \abs{z} < 1 \}$ by a Poisson–Stieltjes integral
where $\mu$ is a Borel measure concentrated on the unit circle $T=\{ z\in\C : \abs{z} = 1 \}$, $\int\rd\mu(\xi)=1$. Then almost-everywhere
4 KB (706 words) - 19:19, 27 July 2012
in the unit disc $ D $
on the boundary circle $ C $(
5 KB (698 words) - 18:20, 26 January 2022
...n|holomorphic functions]] of one complex variable. In the case of the unit circle one has the following relationship between the Cauchy kernel and the [[Hilb
1 KB (198 words) - 20:26, 18 March 2024
...nt lifting theorem and a certain contractive analytic function in the open unit disc. This characterization of all solutions has several different network
on the unit circle whose norm $ \| g \| _ \infty = { \mathop{\rm ess} \sup } \{ {| {g ( e
6 KB (815 words) - 09:51, 26 March 2023
inside the unit circle on the complex plane. Similarly, the dynamical
polynomial $w(z)$ has $m$ roots inside and $n-m$ roots outside the unit
4 KB (607 words) - 02:33, 14 September 2022
lies on the unit circle and there is the spectral decomposition $ U = \int _ {0} ^ {2 \pi } e ^ {
2 KB (255 words) - 08:27, 6 June 2020
on the open unit disc $ | z | < 1 $
...I. Schur, "On power series which are bounded in the interior of the unit circle. II" I. Gohberg (ed.) , ''Methods in Operator Theory and Signal Processing
5 KB (791 words) - 05:51, 13 June 2022
under which the unit circle $ \Gamma = \{ {z } : {| z | = 1 } \} $
is mapped onto itself, the maximum diameter of the image of the circle $ \Gamma _ {R} = \{ {z } : {| z | = R } \} $
4 KB (623 words) - 19:42, 5 June 2020
the circle $ | z | = 1 $
A hyperbolic circle in $ D $
7 KB (952 words) - 12:50, 13 January 2024
where $z\rightarrow 1$ along any path not tangent to the unit circle.
2 KB (258 words) - 12:23, 10 January 2015
...ta$ are real, namely $\theta$ and $1/\theta$, and the rest lie on the unit circle. The field $\mathbf{Q}(\theta)$ is thus a quadratic extension (cf. [[Extens
3 KB (504 words) - 18:43, 14 April 2023
...$ can be characterized as the space of analytic functions $f ( z )$ on the unit disc having [[Taylor series|Taylor series]] representation
...ions (and, more generally, of contractive analytic matrix-functions on the unit disc) in terms of Schur parameters (see [[#References|[a9]]] and [[#Referen
12 KB (1,802 words) - 17:01, 1 July 2020
be a meromorphic function in the unit disc $ D = \{ {z \in \mathbf C } : {| z | < 1 } \} $
on the circle $ \Gamma = \{ {z \in \mathbf C } : {| z | = 1 } \} $
4 KB (660 words) - 08:06, 6 June 2020
Along with these, there are examples of bounded analytic functions in the unit disc $ D $
of measure zero on the unit circle $ \Gamma $.
10 KB (1,496 words) - 08:27, 6 June 2020
The general name for polynomials orthogonal on the circle, over a contour or over an area. Unlike the case of orthogonality in a real
==Orthogonal polynomials on the circle.==
9 KB (1,315 words) - 20:15, 12 January 2024