Cluster sets of analytic multivalued functions
Harbottle, S.
Studia Mathematica, Tome 103 (1992), p. 253-267 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:215904
@article{bwmeta1.element.bwnjournal-article-smv101i3p253bwm,
     author = {S. Harbottle},
     title = {Cluster sets of analytic multivalued functions},
     journal = {Studia Mathematica},
     volume = {103},
     year = {1992},
     pages = {253-267},
     zbl = {0808.30028},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv101i3p253bwm}
}
Harbottle, S. Cluster sets of analytic multivalued functions. Studia Mathematica, Tome 103 (1992) pp. 253-267. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv101i3p253bwm/

[00000] [1] F. Bagemihl, Curvilinear cluster sets of arbitrary functions, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 379-382. | Zbl 0065.06604

[00001] [2] F. Bagemihl and W. Seidel, Some boundary properties of analytic functions, Math. Z. 61 (1954), 186-199. | Zbl 0058.06101

[00002] [3] E. F. Collingwood and A. J. Lohwater, Theory of Cluster Sets, Cambridge University Press, 1966. | Zbl 0149.03003

[00003] [4] B. E. J. Dahlberg, On the radial boundary values of subharmonic functions, Math. Scand. 40 (1977), 301-317. | Zbl 0371.31001

[00004] [5] P. Fatou, Séries trigonométriques et séries de Taylor, Acta Math. 30 (1906), 335-400. | Zbl 37.0283.01

[00005] [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. | Zbl 45.0665.02

[00006] [7] J. E. Littlewood, On functions subharmonic in a circle, II, Proc. London Math. Soc. 28 (1928), 383-394. | Zbl 54.0516.04

[00007] [8] R. Nevanlinna, Analytic Functions, Springer, 1970.

[00008] [9] T. J. Ransford, Open mapping, inversion and implicit function theorems for analytic multivalued functions, Proc. London Math. Soc. (3) 49 (1984), 537-562. | Zbl 0526.46045

[00009] [10] T. J. Ransford, On the range of an analytic multivalued function, Pacific J. Math. 123 (2) (1986), 421-439. | Zbl 0553.30034

[00010] [11] Z. Słodkowski, Analytic set-valued functions and spectra, Math. Ann. 256 (1981), 363-386. | Zbl 0452.46028