The -product of domains in several complex variables
In this article, we investigate the problem of computing the $ * $ ∗ -product of domains in $ \mathbb {C}^N $ C N . Assuming that $ 0\in G\subset \mathbb {C}^N $ 0 ∈ G ⊂ C N is an arbitrary Runge domain and $ 0\in D\subset \mathbb {C}^N $ 0 ∈ D ⊂ C N is a bounded, smooth and linearly convex domain (...
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| Vydáno v: | Complex variables and elliptic equations Ročník 69; číslo 1; s. 35 - 46 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Colchester
Taylor & Francis
02.01.2024
Taylor & Francis Ltd |
| Témata: | |
| ISSN: | 1747-6933, 1747-6941 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | In this article, we investigate the problem of computing the
$ * $
∗
-product of domains in
$ \mathbb {C}^N $
C
N
. Assuming that
$ 0\in G\subset \mathbb {C}^N $
0
∈
G
⊂
C
N
is an arbitrary Runge domain and
$ 0\in D\subset \mathbb {C}^N $
0
∈
D
⊂
C
N
is a bounded, smooth and linearly convex domain (or a non-decreasing union of such ones), we establish a geometric relation between
$ D*G $
D
∗
G
and another domain in
$ \mathbb {C}^N $
C
N
which is 'extremal' (in an appropriate sense) with respect to a special coefficient multiplier dependent only on the dimension N. Next, for N = 2, we derive a characterization of the latter domain expressed in terms of planar geometry. These two results, when combined together, give a formula which allows to calculate
$ D*G $
D
∗
G
for two-dimensional domains D and G satisfying the outlined assumptions. |
|---|---|
| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 1747-6933 1747-6941 |
| DOI: | 10.1080/17476933.2022.2107635 |