...al power dilation with spectrum in $\partial S$. The minimal radius of the circle which is a spectral set for every contraction in a Banach space is equal to
...> J. von Neumann, "Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes" ''Math. Nachr.'' , '''4''' (1951) pp. 258–281</TD></TR><T
2 KB (295 words) - 15:46, 29 December 2018
...a closed curve $L'$ with a cusp at the point $w=1$, touching an arc of the circle $L$ (the image of $K$) at that point; this image is represented in Fig. ban
The function $w=\lambda(\rho t+\alpha)$ maps the exterior of the unit circle in the $t$-plane to the exterior of $L'$. To obtain a Zhukovskii profile of
4 KB (542 words) - 19:58, 4 January 2024
be a bounded regular analytic function in the unit disc $ \Omega = \{ {z \in \mathbf C } : {| z | < 1 } \} $,
...s serve as Lobachevskii straight lines, these being orthogonal to the unit circle (Poincaré's model), and
4 KB (546 words) - 08:06, 6 June 2020
...omeomorphism of the open attainable boundary arc onto some open arc of the circle $|z| = 1$.
1 KB (182 words) - 19:25, 13 December 2015
...n a so-called great circle is obtained as the intersection. A unique great circle can be drawn through any two points $A$ and $B$ on the sphere (Fig. a), exc
...a straight line is the shortest curve between its ends, an arc of a great circle on a sphere is only the shortest curve when it is shorter than the compleme
8 KB (1,389 words) - 15:53, 19 April 2014
...fmath.org/legacyimages/a/a013/a013980/a0139808.png" /> lie inside the unit circle, then equation (*) has the solution
5 KB (730 words) - 17:11, 7 February 2011
...ally onto a standard pair $(D^n,D^m)$ or $(D^n,D_+^m)$, where $D^k$ is the unit ball of the space $\mathbf R^k$ with centre at the origin and $D_+^k$ is th
...imbedding of a circle and an arc into a plane is locally flat; however, a circle or an arc can be imbedded in $\mathbf R^k$ with $k\geq3$ in a manner that i
2 KB (383 words) - 08:32, 19 April 2014
...nd bijectively. The circle property: Under a fractional-linear mapping any circle in $ \overline{\mathbf C}\; $(
i.e. a circle in $ \mathbf C $
13 KB (1,875 words) - 13:58, 17 March 2023
...axis of revolution and the circle described by the centre of its rotating circle.
...f $u$ and $v$, $r$ is the radius vector of the surface $F$, and $n$ is the unit normal to $F$.
2 KB (440 words) - 06:52, 14 July 2024
in the open unit disc whose $ H ^ \infty $-
...hur algorithm can also be used to obtain a Routh or Jury test for the open unit disc, that is, the Schur algorithm can be used to determine whether or not
6 KB (836 words) - 11:17, 30 May 2020
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