{"title":"一个简短的列维(哈托格的逆)问题,连贯性和开放问题的编年史","authors":"J. Noguchi","doi":"10.4310/ICCM.2019.V7.N2.A2","DOIUrl":null,"url":null,"abstract":"Here we chronologically summarize briefly the developments of the Levi (Hartogs' Inverse) Problem together with the notion of coherence and its solution, shedding light on some records which have not been discussed in the past references. In particular, we will discuss K. Oka's unpublished papers 1943 which solved the Levi (Hartogs' Inverse) Problem for unramified Riemann domains of arbitrary dimension $n \\geq 2$, usually referred as it was solved by Oka IX in 1953, H.J. Bremermann and F. Norguet in 1954 for univalent domains, independently. \nAt the end we emphasize an open problem in a ramified case.","PeriodicalId":415664,"journal":{"name":"Notices of the International Congress of Chinese Mathematicians","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A brief chronicle of the Levi (Hartog’s inverse) problem, coherence and open problem\",\"authors\":\"J. Noguchi\",\"doi\":\"10.4310/ICCM.2019.V7.N2.A2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Here we chronologically summarize briefly the developments of the Levi (Hartogs' Inverse) Problem together with the notion of coherence and its solution, shedding light on some records which have not been discussed in the past references. In particular, we will discuss K. Oka's unpublished papers 1943 which solved the Levi (Hartogs' Inverse) Problem for unramified Riemann domains of arbitrary dimension $n \\\\geq 2$, usually referred as it was solved by Oka IX in 1953, H.J. Bremermann and F. Norguet in 1954 for univalent domains, independently. \\nAt the end we emphasize an open problem in a ramified case.\",\"PeriodicalId\":415664,\"journal\":{\"name\":\"Notices of the International Congress of Chinese Mathematicians\",\"volume\":\"8 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-07-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Notices of the International Congress of Chinese Mathematicians\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4310/ICCM.2019.V7.N2.A2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Notices of the International Congress of Chinese Mathematicians","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/ICCM.2019.V7.N2.A2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
在这里,我们按时间顺序简要地总结了李维(哈托格斯逆)问题的发展,以及相干的概念和它的解决方法,揭示了一些在过去的参考文献中没有讨论的记录。特别是,我们将讨论K. Oka 1943年未发表的论文,这些论文解决了任意维$n \geq 2$的未派生黎曼域的Levi (Hartogs' Inverse)问题,通常被称为Oka IX于1953年,H.J. Bremermann和F. Norguet于1954年独立解决了一价域。最后,我们强调了一个分支案例中的开放性问题。
A brief chronicle of the Levi (Hartog’s inverse) problem, coherence and open problem
Here we chronologically summarize briefly the developments of the Levi (Hartogs' Inverse) Problem together with the notion of coherence and its solution, shedding light on some records which have not been discussed in the past references. In particular, we will discuss K. Oka's unpublished papers 1943 which solved the Levi (Hartogs' Inverse) Problem for unramified Riemann domains of arbitrary dimension $n \geq 2$, usually referred as it was solved by Oka IX in 1953, H.J. Bremermann and F. Norguet in 1954 for univalent domains, independently.
At the end we emphasize an open problem in a ramified case.