Note on the Cluster Sets of Analytic Functions

Kiyoshi Noshiro

doi:10.2969/jmsj/00140275

Kiyoshi Noshiro

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1950 Volume 1 Issue 4 Pages 275-281

DOI https://doi.org/10.2969/jmsj/00140275

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Published: 1950 Received: February 15, 1949 Available on J-STAGE: August 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: August 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) "Capacity" means logarithmic capacity in this note.
2) F. Iversen: Sur quelques propriétés des fonction monogénes au voisinage d'un point singulier, Öfv. af Finska Vet-Soc. Förh. 58 (1916). A. Beurling: Étude sur un probleme de majoration, Thèse de Upsal, 1933. Cf, pp. 100-103 K. Kunugi: Sur un thèorème de MM. Seidel-Beurling, Proc. Acad. Tokyo, 15 (1939); Sur un probléme de M. A. Beurling, Proc. Acad. Tokyo, 16 (1940); Sur l'allure d'une function analytique uniforme au voisinage d'un point frontière de son domaine de définition, Jap. Journ. Math. 18 (1942), pp. 1-39.
3) Beurling: 1. c. 2); Kunugi: 1. c. 2).
4) M. Tsuji: On the cluster set of a meromorphic function, Proc. Acad. Tokyo, 19 (1943); On the Riemann surface of an inverse function of a meromorphic function in the neighbourhood of a closed set of capacity zero, Proc. Acad. Tokyo, 19 (1943).
5) Tsuji: 1. c. 4). S. Kametani: The exceptional values of functions with the set of capacity zero of essential singularities, Proc. Acad. Tokyo, 17 (1941), pp. 429-433.
6) K. Noshiro: On the theory of the cluster sets of analytic functions, Journ. Fac. of Sci., Hokkaido lmp. Univ. 6 (1938), pp. 217-231; Cf. Theorem 4.
7) G. C. Evans: Potentials and positively infinite singularities of harmonic functions, Monatshefte für Math und Phys. 43 (1936), pp, 419-424. K. Noshiro : Contributions to the theory of the singularities of analytic functions, Jap. Journ. Moth. 19 (1948), pp. 299-327.
8) L. Ahlfors: Zur Theorie der Überlagerungsflächen, Acta Math. 65 (1935), pp. 157-194. R. Nevanlinna : Eindeutige analytische Funktionen, Berlin, 1936, Cf. p. 323.

Right : 1) “Capacity” means logarithmic capacity in this note.
2) F. Iversen: Sur quelques propriétés des fonction monogénes au voisinage d'un point singulier, Öfv. af Finska Vet-Soc. Förh. 58 (1916). A. Beurling: Étude sur un problème de majoration, Thèse de Upsal, 1933. Cf. pp. 100-103 K. Kunugi: Sur un théorème de MM. Seidel-Beurling, Proc. Acad. Tokyo, 15 (1939); Sur un problème de M. A. Beurling, Proc. Acad. Tokyo, 16 (1940); Sur l'allure d'une fonction analytique uniforme au voisinage d'un point frontière de son domaine de définition, Jap. Journ. Math. 18 (1942), pp. 1-39.
3) Beurling: 1. c. 2); Kunugi: 1. c. 2).
4) M. Tsuji: On the cluster set of a meromorphic function, Proc. Acad. Tokyo, 19 (1943); On the Riemann surface of an inverse function of a meromorphic function in the neighbourhood of a closed set of capacity zero, Proc. Acad. Tokyo, 19 (1943).
5) Tsuji: 1. c. 4). S. Kametani: The exceptional values of functions with the set of capacity zero of essential singularities, Proc. Acad. Tokyo, 17 (1941), pp. 429-433.
6) K. Noshiro: On the theory of the cluster sets of analytic functions, Journ. Fac. of Sci., Hokkaido lmp. Univ. 6 (1938), pp. 217-231; Cf. Theorem 4.
7) G. C. Evans: Potentials and positively infinite singularities of harmonic functions, Monatshefte für Math und Phys. 43 (1936), pp, 419-424. K. Noshiro: Contributions to the theory of the singularities of analytic functions, Jap. Journ. Moth. 19 (1948), pp. 299-327.
8) L. Ahlfors: Zur Theorie der Überlagerungsflächen, Acta Math. 65 (1935), pp. 157-194. R. Nevanlinna: Eindeutige analytische Funktionen, Berlin, 1936, Cf. p. 323.

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