Skip to main content
Log in

Some remarks on cluster sets

  • Published:
Journal d’Analyse Mathématique Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • Ahlfors, L. V. [1], On the characterization of hyperbolic Riemann surfaces.Ann. Acad. Sci. Fenn. A.I.125 (1952), 1–5.

    Google Scholar 

  • Ahlfors, L. V. and A. Beurling [1], Conformal invariants and function-theoretic nul-setsActa Math. 82 (1950), 101–129.

    MathSciNet  Google Scholar 

  • Bagemihl, F. [1], Analytic continuation and the Schwarz reflection principle.Proc. Nat. Acad. Sci. (Wash.)51 (1964), 378–380.

    Article  MATH  MathSciNet  Google Scholar 

  • — [2], Meier points of holomorphic functions.Math. Ann. 155 (1964), 422–424.

    Article  MATH  MathSciNet  Google Scholar 

  • — [3], Some approximation theorems for normal functions.Ann. Acad. Sci. Fenn. A. I.335 (1965), 1–5.

    Google Scholar 

  • Cartwright, M. L. [1], On the asymptotic values of functions with a non-enumerable set of essential singularities.J. London Math. Soc. 11 (1936), 303–306.

    Article  MATH  Google Scholar 

  • Collingwood, E. F. [1], Sur le comportement à la frontière d'une fonction méromorphe dans le cercle unité.C. R. Acad. Sci. (Paris)240 (1955), 1502–1504.

    MATH  MathSciNet  Google Scholar 

  • — [2], on sets of maximum indetermination of analytic functions.Math. Z. 67 (1957), 377–396.

    Article  MATH  MathSciNet  Google Scholar 

  • Dolzhenko, E. P. [1], On the behaviour of meromorphic functions in the vicinity of their singularities (in Russian).Vestnik Moskov. Univ. Ser I, Mat.-Meh. 6 (1964), 3–6.

    Google Scholar 

  • Hällström, G. [1], Über meromorphe Funktionen mit mehrfach zusammenhängenden Existenzgebieten.Acta Acad. Abo. Math. et Phys. 12 (1939), 5–100.

    Google Scholar 

  • Iversen, F. [1], Recherches sur les fonctions inverses des fonctions méromorphes. Thèse. Helsingfors (1914), 1–67.

  • Kametani, S. [1], The exceptional values of functions with the set of capacity zero of essential singularities.Proc. Japan Acad. 17 (1941), 429–433.

    MATH  MathSciNet  Google Scholar 

  • — [2], On Hausdorff's measure and generalized capacities with some of their applications to the theory of functions.Jap. J. Math. 19 (1945), 217–257.

    MATH  MathSciNet  Google Scholar 

  • Kuroda, T. [1], On analytic functions on some Riemann surfaces.Nagoya Math. J. 10 (1956), 27–50.

    MathSciNet  MATH  Google Scholar 

  • Lehto, O. and K. Virtanen [1], Boundary behaviour and normal meromorphic functions.Acta Math. 97 (1957), 47–65.

    Article  MATH  MathSciNet  Google Scholar 

  • Meier, K. [1], Über die Randwerte der meromorphen Funktionen.Math. Ann. 142 (1961), 328–344.

    Article  MATH  MathSciNet  Google Scholar 

  • Noshiro, K. [1], Cluster sets of functions meromorphic in the unit circle.Proc. Nat. Acad. Sci. (Wash.)41 (1955), 398–401.

    Article  MATH  MathSciNet  Google Scholar 

  • — [2], Cluster sets. Springer-Verlag. Berlin. Göttingen. Heidelberg. (1960).

    MATH  Google Scholar 

  • Ohtsuka, M. [1] Dirichlet problems on Riemann surfaces and conformal mapping.Nagoya Math. J. 3 (1951), 91–137.

    MATH  MathSciNet  Google Scholar 

  • Plessner, A. [1], Über das Verhalten analytischer Funktionen am Rande ihrer Definitionsbereiche.J. reine angew. Math. 158 (1927), 219–227.

    MATH  Google Scholar 

  • Pommerenke, C. [1], Über die analytische Kapazität,Arch. Math. 11 (1960), 270–277.

    Article  MATH  MathSciNet  Google Scholar 

  • Tsuji, M. [1], On the cluster set of a meromorphic function.Proc. Japan. Acad. 19 (1943), 60–65.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The work was partially supported by Grant DA-ARO(D)-31-124-G499, University of California, Los Angeles; NSF Grant 25227, University of Illinois; the Hill Foundation Visiting Professor Program, University of Minnesota; NSF GP 1645, Cornell University; AFOSR {393} 63, Harvard University; and the Exchange Professor Program, University of Paris.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Noshiro, K. Some remarks on cluster sets. J. Anal. Math. 19, 283–294 (1967). https://doi.org/10.1007/BF02788722

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02788722

Keywords

Navigation