Kiyoshi Oka


Kiyoshi Oka (岡 潔, Oka Kiyoshi, April 19, 1901 – March 1, 1978) was a Japanese mathematician who did fundamental work in the theory of several complex variables.

Kiyoshi Oka
Kiyoshi Oka in 1973
Born(1901-04-19)April 19, 1901
DiedMarch 1, 1978(1978-03-01) (aged 76)
Alma materKyoto Imperial University
Known forOka coherence theorem
Oka's lemma
Oka–Weil theorem
Plurisubharmonic function
AwardsAsahi Prize (1953)
Japan Academy Prize (1951)
Order of Culture (1960)
Order of the Sacred Treasure, 1st class (1973)
Scientific career
InstitutionsKyoto Imperial University
Hiroshima University
Hokkaido University
Nara Women's University
Kyoto Sangyo University



Oka was born in Osaka. He went to Kyoto Imperial University in 1919, turning to mathematics in 1923 and graduating in 1924.

He was in Paris for three years from 1929, returning to Hiroshima University. He published solutions to the first and second Cousin problems, and work on domains of holomorphy, in the period 1936–1940. He received his Doctor of Science degree from Kyoto Imperial University in 1940. These were later taken up by Henri Cartan and his school, playing a basic role in the development of sheaf theory.

The Oka–Weil theorem is due to a work of André Weil in 1935 and Oka's work in 1937.[1]

Oka continued to work in the field, and proved Oka's coherence theorem in 1950. Oka's lemma is also named after him.

He was a professor at Nara Women's University from 1949 to retirement at 1964. He received many honours in Japan.




    • Oka, Kiyoshi (1961). Sur les fonctions analytiques de plusieurs variables (in French). Tokyo, Japan: Iwanami Shoten. p. 234. - Includes bibliographical references.
    • Oka, Kiyoshi (1983). Sur les fonctions analytiques de plusieurs variables (in French) (Nouv. ed. augmentee. ed.). Tokyo, Japan: Iwanami. p. 246.
    • Oka, Kiyoshi (1984). Reinhold Remmert (ed.). Kiyoshi Oka Collected Papers. Translated by Raghavan Narasimhan. Commentary: Henri Cartan. Springer-Verlag. p. 223. ISBN 0-387-13240-6.

Selected papers (Sur les fonctions analytiques de plusieurs variables)

  1. Oka, Kiyoshi (1936). "Domaines convexes par rapport aux fonctions rationnelles". Journal of Science of the Hiroshima University. 6: 245–255. doi:10.32917/hmj/1558749869. PDF TeX
  2. Oka, Kiyoshi (1937). "Domaines d'holomorphie". Journal of Science of the Hiroshima University. 7: 115–130. doi:10.32917/hmj/1558576819. PDF TeX.
  3. Oka, Kiyoshi (1939). "Deuxième problème de Cousin". Journal of Science of the Hiroshima University. 9: 7–19. doi:10.32917/hmj/1558490525. PDF TeX.
  4. Oka, Kiyoshi (1941). "Domaines d'holomorphie et domaines rationnellement convexes". Japanese Journal of Mathematics. 17: 517–521. doi:10.4099/jjm1924.17.0_517. PDF TeX.
  5. Oka, Kiyoshi (1941). "L'intégrale de Cauchy". Japanese Journal of Mathematics. 17: 523–531. PDF TeX.
  6. Oka, Kiyoshi (1942). "Domaines pseudoconvexes". Tôhoku Mathematical Journal. 49: 15–52. PDF TeX.
  7. Oka, Kiyoshi (1950). "Sur quelques notions arithmétiques". Bulletin de la Société Mathématique de France. 78: 1–27. doi:10.24033/bsmf.1408. PDF TeX.
  8. Oka, Kiyoshi (1951). "Sur les Fonctions Analytiques de Plusieurs Variables, VIII--Lemme Fondamental". Journal of the Mathematical Society of Japan. 3: 204–214, pp. 259–278. doi:10.2969/jmsj/00310204. PDF TeX.
  9. Oka, Kiyoshi (1953). "Domaines finis sans point critique intérieur". Japanese Journal of Mathematics. 27: 97–155. doi:10.4099/jjm1924.23.0_97. PDF TeX.
  10. Oka, Kiyoshi (1962). "Une mode nouvelle engendrant les domaines pseudoconvexes". Japanese Journal of Mathematics. 32: 1–12. doi:10.4099/jjm1924.32.0_1. PDF TeX.
  11. Oka, Kiyoshi (1934). "Note sur les familles de fonctions analytiques multiformes etc". Journal of Science of the Hiroshima University. Ser.A 4: 93–98. doi:10.32917/hmj/1558749763. PDF TeX.
  12. Oka, Kiyoshi (1941). "Sur les domaines pseudoconvexes". Proc. Imp. Acad. Tokyo. 17 (1): 7–10. doi:10.3792/pia/1195578912. PDF TeX.
  13. Oka, Kiyoshi (1949). "Note sur les fonctions analytiques de plusieurs variables". Kodai Math. Sem. Rep. (5–6): 15–18. doi:10.2996/kmj/1138833536. PDF TeX.


  1. ^ Fornaess, J.E.; Forstneric, F; Wold, E.F (2020). "The Legacy of Weierstrass, Runge, Oka–Weil, and Mergelyan". In Breaz, Daniel; Rassias, Michael Th. (eds.). Advancements in Complex Analysis – Holomorphic Approximation. Springer Nature. pp. 133–192. arXiv:1802.03924. doi:10.1007/978-3-030-40120-7. ISBN 978-3-030-40119-1. S2CID 242185140.