-
distance in Cn. When n > 1 {\displaystyle n>1} , open
balls and open
polydiscs are not
biholomorphically equivalent, that is,
there is no biholomorphic...
- 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...
- 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...
- } . {\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...
- 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...
- 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...
- 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}}...
- ( 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...
-
induction step. QED The
previous lemma can be
generalised by
admitting polydiscs with ε k = + ∞ {\displaystyle \varepsilon _{k}=+\infty } for some of the...
