Definition of Polydiscs. Meaning of Polydiscs. Synonyms of Polydiscs

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Definition of Polydiscs

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Meaning of Polydiscs from wikipedia

- distance in Cn. When n > 1 {\displaystyle n>1} , open balls and open polydiscs are not biholomorphically equivalent, that is, there is no biholomorphic...
- 4.339. PMC 528447. PMID 16578475. Rudin, Walter (1967). "Zero-sets in polydiscs". Bull. Amer. Math. Soc. 73 (4): 580–583. doi:10.1090/s0002-9904-1967-11758-0...
- The Cauchy integral formula holds only for polydiscs, and in the domain of several complex variables, polydiscs are only one of many possible domains, so...
- } . {\displaystyle \left\{z\in \mathbb {C} ^{n}:\|z\|<1\right\}.} the polydisc { z = ( z 1 , … , z n ) ∈ C n : | z j | < 1   ∀ j = 1 , … , n } . {\displaystyle...
- the one variable case, this follows from Cauchy's integral formula in polydiscs. § Related estimate and its consequence also continue to be valid in several...
- ( U ) {\displaystyle {\mathcal {O}}_{X}^{\mathrm {an} }(U)} for every polydisc U is a suitable quotient of the space of holomorphic functions on U. For...
- variables, the Cauchy integral formula can be generalized to polydiscs. Let D be the polydisc given as the Cartesian product of n open discs D1, ..., Dn:...
- different in higher dimensions. For example, open unit balls and open unit polydiscs are not biholomorphically equivalent for n > 1. {\displaystyle n>1.} In...
- induction step. QED The previous lemma can be generalised by admitting polydiscs with ε k = + ∞ {\displaystyle \varepsilon _{k}=+\infty } for some of the...
- connectedness. The basic rigid analytic object is the n-dimensional unit polydisc, whose ring of functions is the Tate algebra T n {\displaystyle T_{n}}...