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
...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
...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