Oka's lemma (original) (raw)
In mathematics, Oka's lemma, proved by Kiyoshi Oka, states that in a domain of holomorphy in , the function is plurisubharmonic, where is the distance to the boundary. This property shows that the domain is pseudoconvex. Historically, this lemma was first shown in the Hartogs domain in the case of two variables, also Oka's lemma is the inverse of Levi's problem (unramified Riemann domain ). Therefore, Oka himself calls Levi's problem "problème inverse de Hartogs", and Levi's problem is occasionally called Hartogs' Inverse Problem.
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| dbo:abstract | In mathematics, Oka's lemma, proved by Kiyoshi Oka, states that in a domain of holomorphy in , the function is plurisubharmonic, where is the distance to the boundary. This property shows that the domain is pseudoconvex. Historically, this lemma was first shown in the Hartogs domain in the case of two variables, also Oka's lemma is the inverse of Levi's problem (unramified Riemann domain ). Therefore, Oka himself calls Levi's problem "problème inverse de Hartogs", and Levi's problem is occasionally called Hartogs' Inverse Problem. (en) 数学における岡の補題（おかのほだい、英: Oka's lemma）とは、岡潔によって証明されたある補題のことを言う。その補題では、Cn 内のある正則領域において、函数 –log d(z) は多重劣調和であると述べられている。ここで d は境界からの距離を表す。この性質により、そのような領域は擬凸であることが示される。 (ja) Inom matematiken är Okas lemma, bevisad av , ett resultat som säger att i en i Cn är funktionen –log d(z) , där d betecknar avståndet till randen. Detta bevisar att domänen är . (sv) |
| dbo:wikiPageExternalLink | https://www.nara-wu.ac.jp/aic/gdb/nwugdb/oka/ko_ron/pdf/ko-f9.pdf https://www.nara-wu.ac.jp/aic/gdb/nwugdb/oka/ko_ron/tex/ko-f9.tex https://www.nara-wu.ac.jp/aic/gdb/nwugdb/oka/ko_ron/f/n09/p001.html%7Cdoi=10.4099/jjm1924.23.0_97%7Cdoi-access=free https://projecteuclid.org/euclid.ijm/1380287467 |
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| dcterms:subject | dbc:Lemmas_in_analysis dbc:Theorems_in_complex_analysis |
| gold:hypernym | dbr:Distance |
| rdf:type | dbo:Agent yago:WikicatLemmas yago:Abstraction100002137 yago:Communication100033020 yago:Lemma106751833 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 |
| rdfs:comment | In mathematics, Oka's lemma, proved by Kiyoshi Oka, states that in a domain of holomorphy in , the function is plurisubharmonic, where is the distance to the boundary. This property shows that the domain is pseudoconvex. Historically, this lemma was first shown in the Hartogs domain in the case of two variables, also Oka's lemma is the inverse of Levi's problem (unramified Riemann domain ). Therefore, Oka himself calls Levi's problem "problème inverse de Hartogs", and Levi's problem is occasionally called Hartogs' Inverse Problem. (en) 数学における岡の補題（おかのほだい、英: Oka's lemma）とは、岡潔によって証明されたある補題のことを言う。その補題では、Cn 内のある正則領域において、函数 –log d(z) は多重劣調和であると述べられている。ここで d は境界からの距離を表す。この性質により、そのような領域は擬凸であることが示される。 (ja) Inom matematiken är Okas lemma, bevisad av , ett resultat som säger att i en i Cn är funktionen –log d(z) , där d betecknar avståndet till randen. Detta bevisar att domänen är . (sv) |
| rdfs:label | Oka's lemma (en) 岡の補題 (ja) Okas lemma (sv) |
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| prov:wasDerivedFrom | wikipedia-en:Oka's_lemma?oldid=1029474292&ns=0 |
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