# Cluster sets of analytic multivalued functions

Studia Mathematica (1992)

- Volume: 101, Issue: 3, page 253-267
- ISSN: 0039-3223

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topHarbottle, S.. "Cluster sets of analytic multivalued functions." Studia Mathematica 101.3 (1992): 253-267. <http://eudml.org/doc/215904>.

@article{Harbottle1992,

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.},

author = {Harbottle, S.},

journal = {Studia Mathematica},

keywords = {cluster sets; multivalued functions},

language = {eng},

number = {3},

pages = {253-267},

title = {Cluster sets of analytic multivalued functions},

url = {http://eudml.org/doc/215904},

volume = {101},

year = {1992},

}

TY - JOUR

AU - Harbottle, S.

TI - Cluster sets of analytic multivalued functions

JO - Studia Mathematica

PY - 1992

VL - 101

IS - 3

SP - 253

EP - 267

AB - 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.

LA - eng

KW - cluster sets; multivalued functions

UR - http://eudml.org/doc/215904

ER -

## References

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- [2] F. Bagemihl and W. Seidel, Some boundary properties of analytic functions, Math. Z. 61 (1954), 186-199. Zbl0058.06101
- [3] E. F. Collingwood and A. J. Lohwater, Theory of Cluster Sets, Cambridge University Press, 1966. Zbl0149.03003
- [4] B. E. J. Dahlberg, On the radial boundary values of subharmonic functions, Math. Scand. 40 (1977), 301-317. Zbl0371.31001
- [5] P. Fatou, Séries trigonométriques et séries de Taylor, Acta Math. 30 (1906), 335-400. Zbl37.0283.01
- [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. Zbl45.0665.02
- [7] J. E. Littlewood, On functions subharmonic in a circle, II, Proc. London Math. Soc. 28 (1928), 383-394. Zbl54.0516.04
- [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. Zbl0526.46045
- [10] T. J. Ransford, On the range of an analytic multivalued function, Pacific J. Math. 123 (2) (1986), 421-439. Zbl0553.30034
- [11] Z. Słodkowski, Analytic set-valued functions and spectra, Math. Ann. 256 (1981), 363-386. Zbl0452.46028

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