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367:{\displaystyle \{w=(w_{1},w_{2},\dots ,w_{n})\in {\mathbf {C} }^{n}:\vert z_{k}-w_{k}\vert <r_{k},{\mbox{ for all }}k=1,\dots ,n\}.}
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Poincare, H, Les fonctions analytiques de deux variables et la representation conforme, Rend. Circ. Mat. Palermo23 (1907), 185-220
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449:{\displaystyle \{w\in \mathbf {C} ^{n}:\lVert z-w\rVert <r\}.}
188:{\displaystyle D(z_{1},r_{1})\times \dots \times D(z_{n},r_{n}).}
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Several
Complex Variables and the Geometry of Real Hypersurfaces
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John P D'Angelo, D'Angelo P D'Angelo (Jan 6, 1993).
504:biholomorphically equivalent, that is, there is no
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637:Creative Commons Attribution/Share-Alike License
377:One should not confuse the polydisc with the
99:, then an open polydisc is a set of the form
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590:Function Theory of Several Complex Variables
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508:between the two. This was proven by
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48:More specifically, if we denote by
198:It can be equivalently written as
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592:. American Mathematical Society.
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588:Steven G Krantz (Jan 1, 2002).
635:, which is licensed under the
512:in 1907 by showing that their
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25:In the theory of functions of
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516:have different dimensions as
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16:Cartesian product of discs
653:Several complex variables
27:several complex variables
558:logarithmically convex
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493:{\displaystyle n>1}
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76:{\displaystyle D(z,r)}
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542:{\displaystyle n=2}
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91:and radius
31:mathematics
21:Duocylinder
633:PlanetMath
567:References
518:Lie groups
459:Here, the
19:See also:
549:the term
432:‖
426:−
420:‖
402:∈
379:open ball
350:…
299:−
266:∈
247:…
148:×
145:⋯
142:×
647:Category
629:polydisc
510:Poincaré
35:polydisc
463:is the
95:in the
615:
596:
551:bidisc
523:When
474:When
43:discs
37:is a
613:ISBN
594:ISBN
485:>
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83:the
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.