| Title:
|
Trivial generators for nontrivial fibres (English) |
| Author:
|
Carlsson, Linus |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
133 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
121-131 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Pseudoconvex domains are exhausted in such a way that we keep a part of the boundary fixed in all the domains of the exhaustion. This is used to solve a problem concerning whether the generators for the ideal of either the holomorphic functions continuous up to the boundary or the bounded holomorphic functions, vanishing at a point in $\mathbb{C}^{n}$ where the fibre is nontrivial, has to exceed $n$. This is shown not to be the case. (English) |
| Keyword:
|
holomorphic function |
| Keyword:
|
Banach algebra |
| Keyword:
|
generator |
| MSC:
|
32A65 |
| MSC:
|
32W05 |
| MSC:
|
46J20 |
| idZBL:
|
Zbl 1199.32021 |
| idMR:
|
MR2428308 |
| DOI:
|
10.21136/MB.2008.134053 |
| . |
| Date available:
|
2009-09-24T22:35:17Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134053 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[4] So-Chin Chen, Mei-Chi Shaw: Partial Differential Equations in Several Complex Variables, vol. 19 of AMS/IP Studies in Advanced Mathematics.American Mathematical Society, Providence, RI, 2001. MR 1800297 |
| Reference:
|
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| Reference:
|
[6] Andrew M. Gleason: Finitely generated ideals in Banach algebras.J. Math. Mech. 13 (1964), 125–132. MR 0159241 |
| Reference:
|
[7] Pengfei Guan: The extremal function associated to intrinsic norms.Ann. Math. 156 (2002), 197–211. MR 1935845 |
| Reference:
|
[8] Gennadi Henkin, Jürgen Leiterer: Theory of Functions on Complex Manifolds.Monographs in Mathematics vol. 79, Birkhäuser, Basel, 1984. MR 0774049 |
| Reference:
|
[9] Marek Jarnicki, Peter Pflug: Extension of Holomorphic Functions.Expositions in Mathematics vol. 34, Walter de Gruyter, Berlin, 2000. MR 1797263 |
| Reference:
|
[10] Nils Øvrelid: Generators of the maximal ideals of $A(\bar{D})$.Pacific J. Math. 39 (1971), 219–223. MR 0310292, 10.2140/pjm.1971.39.219 |
| . |
