Polydisc
From Encyclopedia of Mathematics
polycylinder
A region
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in a complex space ,
, which is the topological product of
discs
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The point is the centre of the polydisc
,
,
,
, is its polyradius. With
,
one obtains the unit polydisc. The distinguished boundary of
is the set
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which is a part of its complete topological boundary . A polydisc is a complete Reinhardt domain.
A natural generalization of the concept of a polydisc is that of a polyregion (polycircular region, generalized polycylinder) , which is the topological product of, in general multiply-connected, regions
,
. The boundary
of a polyregion
consists of
sets of dimension
:
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the common part of which is the -dimensional distinguished boundary of
:
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Comments
References
[a1] | W. Rudin, "Function theory in polydiscs" , Benjamin (1969) |
How to Cite This Entry:
Polydisc. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Polydisc&oldid=48234
Polydisc. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Polydisc&oldid=48234
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article