ArticleOriginal scientific text

Title

Cluster sets of analytic multivalued functions

Authors 1

Affiliations

  1. 2, Berwick Hill Road, Ponteland, Newcastle Upon Tyne, NE20 9UU, England

Abstract

Classical theorems about the cluster sets of holomorphic functions on the unit disc are extended to the more general setting of analytic multivalued functions, and examples are given to show that these extensions cannot be improved.

Bibliography

  1. F. Bagemihl, Curvilinear cluster sets of arbitrary functions, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 379-382.
  2. F. Bagemihl and W. Seidel, Some boundary properties of analytic functions, Math. Z. 61 (1954), 186-199.
  3. E. F. Collingwood and A. J. Lohwater, Theory of Cluster Sets, Cambridge University Press, 1966.
  4. B. E. J. Dahlberg, On the radial boundary values of subharmonic functions, Math. Scand. 40 (1977), 301-317.
  5. P. Fatou, Séries trigonométriques et séries de Taylor, Acta Math. 30 (1906), 335-400.
  6. E. Lindelöf, Sur un principe général de l'analyse et ses applications à la théorie de la représentation conforme, Acta Soc. Sci. Fenn. 46 (4) (1915), 1-35.
  7. J. E. Littlewood, On functions subharmonic in a circle, II, Proc. London Math. Soc. 28 (1928), 383-394.
  8. R. Nevanlinna, Analytic Functions, Springer, 1970.
  9. T. J. Ransford, Open mapping, inversion and implicit function theorems for analytic multivalued functions, Proc. London Math. Soc. (3) 49 (1984), 537-562.
  10. T. J. Ransford, On the range of an analytic multivalued function, Pacific J. Math. 123 (2) (1986), 421-439.
  11. Z. Słodkowski, Analytic set-valued functions and spectra, Math. Ann. 256 (1981), 363-386.
Pages:
253-267
Main language of publication
English
Received
1991-01-11
Published
1992
Exact and natural sciences