Difference between revisions of "Bicylindrical domain"
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| + | $#C+1 = 10 : ~/encyclopedia/old_files/data/B016/B.0106130 Bicylindrical domain | ||
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| − | A special case of a bicylindrical domain is the bidisc (bicylinder) | + | A domain $ D $ |
| + | in the complex space $ \mathbf C ^ {2} $ | ||
| + | that can be represented in the form of the Cartesian product of two planar domains $ D _ {1} $ | ||
| + | and $ D _ {2} $, | ||
| + | i.e. | ||
| + | |||
| + | $$ | ||
| + | D = \{ {(z _ {1} , z _ {2} ) } : { | ||
| + | z _ {1} \in D _ {1} , z _ {2} \in D _ {2} } \} | ||
| + | . | ||
| + | $$ | ||
| + | |||
| + | A special case of a bicylindrical domain is the bidisc (bicylinder) $ B(a, r) = \{ {(z _ {1} , z _ {2} ) } : {| z _ {1} - a _ {1} | < r _ {1} , | z _ {2} - a _ {2} | < r _ {2} } \} $ | ||
| + | of radius $ r = (r _ {1} , r _ {2} ) $ | ||
| + | with centre at $ a = (a _ {1} , a _ {2} ) $. | ||
| + | The Cartesian product of $ n $( | ||
| + | for $ n \geq 3 $) | ||
| + | planar domains is said to be a polycylindrical domain. A polydisc (polycylinder) is defined in a similar way. | ||
Latest revision as of 10:59, 29 May 2020
A domain $ D $
in the complex space $ \mathbf C ^ {2} $
that can be represented in the form of the Cartesian product of two planar domains $ D _ {1} $
and $ D _ {2} $,
i.e.
$$ D = \{ {(z _ {1} , z _ {2} ) } : { z _ {1} \in D _ {1} , z _ {2} \in D _ {2} } \} . $$
A special case of a bicylindrical domain is the bidisc (bicylinder) $ B(a, r) = \{ {(z _ {1} , z _ {2} ) } : {| z _ {1} - a _ {1} | < r _ {1} , | z _ {2} - a _ {2} | < r _ {2} } \} $ of radius $ r = (r _ {1} , r _ {2} ) $ with centre at $ a = (a _ {1} , a _ {2} ) $. The Cartesian product of $ n $( for $ n \geq 3 $) planar domains is said to be a polycylindrical domain. A polydisc (polycylinder) is defined in a similar way.
How to Cite This Entry:
Bicylindrical domain. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bicylindrical_domain&oldid=46052
Bicylindrical domain. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bicylindrical_domain&oldid=46052
This article was adapted from an original article by M. Shirinbekov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article