Cluster sets of analytic multivalued functions

• Autorzy: S. R. Harbottle
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 30D40: Cluster sets, prime ends, boundary behavior
• 30G30: Other generalizations of analytic functions (including abstract-valued functions)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1991-1992
• Tom: 101
• Numer: 3
• Strony: 253-267

Daty

wydano

1992

otrzymano

1991-01-11

Twórcy

autor

S. R. Harbottle

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

Bibliografia

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• [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.
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