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Generalization of Levi-Oka’s Theorem Concerning Meromorphic Functions

Published online by Cambridge University Press:  22 January 2016

Joji Kajiwara and
Eiichi Sakai
Joji Kajiwara
Affiliation:
Mathematical Institute, Nagoya University
Eiichi Sakai
Affiliation:
Mathematical Institute, Kanazawa University
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As Fuks [3] stated, every domain of holomorphy or meromorphy over Cn is analytically convex in the sense of Hartogs. Oka [6] proved that every domain over Cn analytically convex in the sense of Hartogs is a domain of holomorphy. Therefore a domain of meromorphy over Cn coincides with a domain of holomorphy over Cn .

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 29 , March 1967, pp. 75 - 84
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1967

References

[1] Cartan, H. und Thullen, P., Zur Théorie der Singularitäten den Funktionen mehrererkomplexen Veränderlichen: Regularitäts-und Konvergenz-bereiche, Math. Ann., 106 (1932), 617–647.CrossRefGoogle Scholar
[2] Docquier, F. und Grauert, H., Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeit, Math. Ann., 140 (1960), 94–123.CrossRefGoogle Scholar
[3] Fuks, B. A., Special chapters of theory of analytic functions of several complex variables, Moscow (1963).Google Scholar
[4] Hitotumatu, S. and Kôta, O., Ideals of meromorphic functions of several complex variables, Math. Ann., 125 (1952), 119–126.Google Scholar
[5] Malgrange, B., Lectures on the theory of functions of several complex variables, Tata Inst. Fund. Res. Bombay, (1958).Google Scholar
[6] Oka, K., Sur les fonctions analytiques de plusieur variables IX: Domaines finis sans point critique intérieur, Jap. J. Math., 27 (1953), 67–155.Google Scholar
[7] Okuda, H. and Sakai, E., On the continuation theorem of Levi and the radius of meromorphy, Mem. Fac. Sci. Kyushu Univ. (A), 11 (1957), 65–73.Google Scholar
[8] Siegel, C. L., Analytic functions of several complex variables, Priceton Lecture (1949/50).Google Scholar