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...th>. The classical Poisson formula for a bounded harmonic function on the disc has the form ...e disc determines a function on the group of Möbius transformations of the disc by setting {{math|''F''(''g'') {{=}} ''f''(''g''(0))}}. Then the Poisson f ...

...[sequence]] of [[Holomorphic function|holomorphic]], [[Compact convergence|compact]] [[Uniform convergence#Definition|locally uniformly convergent]] functions ...a connected [[open set]] ''G'' that converge uniformly on [[Compact space|compact]] subsets of ''G'' to a holomorphic function ''f'' which is not constantly ...

...ing the ambient space <math>\mathbb{S}^{n+1}</math> by a simply-connected, compact symmetric space. Some results in this direction are due to [[Wu-Chung Hsian ...gular point of a minimal hypersurface necessarily different from that of a disc? ...

A family <math>\mathcal F</math> of functions [[meromorphic]] on the unit disc <math>\Delta</math> is not normal if and only if there exist: spherically uniformly on compact subsets of <math>C,</math> where <math>g</math> is a nonconstant meromorphi ...

...<math>\partial M</math> is non-empty and <math>M</math> is [[compact space|compact]]. ...</math> is <math>M \times S^k</math>. Even more generally, the double of a disc bundle over a manifold is a sphere bundle over the same manifold. More conc ...

|{{Hlist|[[Compact disc|CD]]|[[Music download|Download]]}} |{{Hlist|[[Compact disc|CD]]|[[Music download|Download]]}} ...

...es|classification theorem for surfaces]] states that every [[compact space|compact]] [[connected space|connected]] two-dimensional manifold is [[homeomorphism ...>''2''</sup>'''. Another surface of genus zero is the [[disk (mathematics)|disc]]. ...

...ath> are the polar coordinates of the point <math>(x,y)</math> on the unit disc map. ...is the intensity of the pixel at the point <math>(x,y)</math> on the unit disc mapped from image <math>i</math>. ...

...lysis]]. Namely, if ''f'' is a [[holomorphic function]] on the [[open unit disc]] ''D'' in the [[complex number]]s '''C''' such that ''f''(0) = 0 and |''f' for all holomorphic maps ''f'' from the unit disc ''D'' to ''X'', where <math> \rho(x,y)</math> denotes distance in the Poinc ...

...{val|44.1|ul=kHz}} audio sampling rate is widely used due to the [[compact disc]] (CD) format, dating back to its use by [[Sony]] from 1979. ...mat]]s which were originally created from material [[Ripping|ripped]] from compact discs. ...

A ''bordered Riemann surface'' ''X'' can be defined as a region on a [[compact Riemann surface]] whose boundary ∂''X'' consists of finitely many disjoint ...is an open Riemann surface, for example the [[complex plane]] or the unit disc, and let ''Z'' be equipped with a conformal metric ''ds''. We say that (''Z ...

...ates that given a positive harmonic function <math>f</math> on the [[unit disc]] <math>\mathbb D = \{ z \in \mathbb C : |z| < 1\}</math> (that is, <math>\ ...s]] associated to <math>\Delta</math> (i.e. the [[Brownian motion]] on the disc with the Poincaré Riemannian metric), then the process <math>f(W_t)</math> ...

...e mediums. These errors may be due to physical damage such as scratch on a disc or a stroke of lightning in case of wireless channels. They are not indepen It is often useful to have a compact definition of a burst error, that encompasses not only its length, but also ...

In [[astrophysics]], the '''chirp mass''' of a compact binary system determines the [[leading-order]] orbital evolution of the sys .../002 |arxiv=gr-qc/9602024 |title=Gravitational waveforms from inspiralling compact binaries to second-post-Newtonian order |bibcode=1996CQGra..13..575B |pages ...

{{Compact ToC|short1|sym=yes|x=[[#XYZ|XYZ]]|y=|z=|seealso=yes|refs=yes}} ...[Alaoglu's theorem]] states that the closed unit ball in a normed space is compact in the [[weak-* topology]].}} ...

...pair cascade in a strong electric and radiation field.<ref>Camenzind, M.: "Compact objects in Astrophysics" (Springer 2007, {{ISBN|978-3-540-25770-7}}), p. 50 The Blandford–Znajek process requires an [[accretion disc]] with a strong [[Toroidal and poloidal|poloidal]] magnetic field around a ...

...ning fixed points and iterations of [[holomorphic mapping]]s of the [[unit disc]] in the [[complex numbers]] into itself. The result was proved independent ...losure of ''D'' such that the iterates of ''f'' tend to ''z'' uniformly on compact subsets of ''D''. If ''z'' lies in ''D'', it is the unique fixed point of ' ...

...is an open subset of the unit disk mapping homeomorphically onto the open disc. If ''N'' > 1, its complement would also have to be open, contradicting con ...But then the [[Arzelà–Ascoli theorem]] implies these homeomorphisms form a compact subset in C('''T'''). The non-linear functional Λ is continuous on this sub ...

...>f(z) = z^2</math> consists precisely of the complement of the closed unit disc: ...nk=Lasse Rempe-Gillen |arxiv=2006.16946 |title=Escaping sets are not sigma-compact |journal=[[Proceedings of the American Mathematical Society]] |date=2020 |v ...

...to any larger disk |''z''| < ''R'' with ''R'' > 1. Accordingly in the unit disc is compact, indeed it is given by an operator with smooth kernel because ''P'' and ''T ...