...Toeplitz operator]]) whose symbol $f$ is a continuous function on the unit circle. In this case $\sigma _ { \text { lre } } ( T )$ is the range of $f$, and $
5 KB (812 words) - 17:00, 1 July 2020
...the second through the smaller angle is the direction of traversal on the circle. In $E^3$, a frame can be related to a screw. The first vector goes in the
...tangent plane at the point $x_0$ (for example, a rotation direction on the circle can be defined by choosing one tangent vector). If $M$ has a boundary and i
18 KB (2,980 words) - 17:05, 13 June 2020
...s to consideration of examples (a straight line, an interval, a polygon, a circle, etc.). Since it does not have general methods at its disposal, elementary
...ex of each end of the interval is equal to one. b) At each of its points a circle has ramification index two. c) A curve consisting of $ n $
19 KB (2,971 words) - 19:30, 26 March 2023
...algebra|Lie algebra]] consisting of the differential operators on the unit circle $S ^ { 1 }$ which have a finite Fourier expansion (cf. also [[Fourier serie
...ghest weight modules over the Lie algebra of differential operators on the circle" ''Comm. Math. Phys.'' , '''157''' (1993) pp. 429–457</td></tr><tr><td
9 KB (1,398 words) - 10:21, 11 November 2023
...genus, Willmore also showed that for anchor rings, obtained by rotating a circle of radius $r$ about an axis in its plane at distance $R > r$ from its ce
...nding Euler equation. In the particular case when the ambient space is the unit sphere $S ^ { 3 } \subset \mathbf{R} ^ { 4 }$, the Euler equation becomes $
8 KB (1,192 words) - 16:56, 1 July 2020
Let $D = \{ z \in \mathbf{C} : | z | < 1 \}$ be the unit disc and let, for $1 \leq p < \infty$, $H ^ { p }$ denote the space of holo
...he Poisson kernel (cf. also [[Poisson integral|Poisson integral]]) for the unit disc. A function $\varphi$, defined on $[ - \pi , \pi ]$, belongs to $\oper
18 KB (2,656 words) - 05:17, 15 February 2024
a) $n = 1$. If $M = \Gamma$ is a smooth arc connecting two points of the unit circle $\gamma = \{ z _ { 1 } : | z _ { 1 } | = 1 \}$ and lying inside $\gamma$ an
7 KB (996 words) - 09:31, 3 February 2024
...distributed outside and inside the unit disc without intersecting the unit circle.
with the unit circle is countable, then each bounded uniformly-continuous solution on $ J $
26 KB (3,943 words) - 20:22, 16 January 2024
...\alpha \in S ^ { 1 }$ and all $p \in \bf R$, where $S ^ { 1 }$ is the unit circle in $\mathbf{R} ^ { 2 }$, is known to be:
8 KB (1,283 words) - 20:10, 10 January 2021
For the trigonometric moment problem, $I$ is the unit circle in the complex plane and the polynomials are complex, so that "positive de
6 KB (888 words) - 18:32, 21 December 2020
is the imaginary unit; $ 1 $
is a unit vector in $ {\mathcal H} $(
8 KB (1,210 words) - 08:23, 6 June 2020
...e of the pencil. The power of the centre of the pencil with respect to any circle of the pencil is the same and is called the power of the pencil. If the $
axis is the radical axis of the pencil, then the equation of an arbitrary circle of the pencil has the form
20 KB (3,056 words) - 08:25, 6 June 2020
...g when the curve $C$ can be rationally parametrized. For example, the unit circle $X ^ { 2 } + Y ^ { 2 } = 1$ has the rational parametrization
...ine of slope $t$ through the point $( - 1,0 )$ and notes that it meets the circle in the variable point
16 KB (2,510 words) - 17:43, 1 July 2020
...f non-intersecting circles (and here a straight line is considered to be a circle of infinite radius) onto a domain $ G _ {2} $
enters in its description. In particular, the general form of mappings of the unit disc $ D = \{ {z } : {| z | < 1 } \} $
28 KB (4,208 words) - 17:46, 4 June 2020
is the circle of radius $ \rho $
is equal to the arithmetic average of its values on any sufficiently small circle $ L \subset D $
26 KB (3,804 words) - 08:11, 13 February 2022
...lde{A}$ is the algebra with involution obtained from $A$ by addition of a unit element, there exists a unique norm on $\tilde{A} $ which converts $\tilde
...tructed. Any $\Cstar$-algebra $A$ has an approximate unit, located in the unit ball of $A$ and formed by positive elements of $A$. If $I$, $J$ are closed
15 KB (2,316 words) - 21:05, 20 April 2012
1) $n = 1$. Let $D$ be the domain bounded by a part of the unit circle $\gamma = \{ z _ { 1 } : | z _ { 1 } | = 1 \}$ and a smooth open arc $\Gamm
6 KB (978 words) - 17:44, 1 July 2020
...ed space; if a point is removed, then the remainder is connected, but if a circle that does not reduce to a point is removed, then the remainder is disconnec
...' if for any two points $x,y \in X$ there is a continuous map $p$ from the unit interval $[0,1]$ with the usual topology to $X$ such that $p(0) = x$ and $p
8 KB (1,209 words) - 06:00, 22 April 2023
is a regular [[Analytic function|analytic function]] in the unit disc $ D= \{ {z = re ^ {i \theta } \in \mathbf C } : {| z | < 1 } \} $
is an arbitrary set of positive measure on the circle $ \Gamma = \{ {z = e ^ {i \theta } } : {| z | = 1 } \} $,
6 KB (965 words) - 08:11, 6 June 2020
...n circular optical elements can be quantified by mean-square deviation per unit area. Given a function $f$ on $D$ and $n \in \mathbf{N} _ { 0 } = \{ 0,1,2
...mathbf{N} _ { 0 }$ and $m = n - 2 j$ with $j = 0 , \dots , n$, the Zernike circle polynomial is
8 KB (1,192 words) - 08:49, 10 November 2023