Cluster sets of analytic multivalued functions

S. Harbottle

Studia Mathematica (1992)

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

Abstract

top
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.

How to cite

top

Harbottle, 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

top
  1. [1] F. Bagemihl, Curvilinear cluster sets of arbitrary functions, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 379-382. Zbl0065.06604
  2. [2] F. Bagemihl and W. Seidel, Some boundary properties of analytic functions, Math. Z. 61 (1954), 186-199. Zbl0058.06101
  3. [3] E. F. Collingwood and A. J. Lohwater, Theory of Cluster Sets, Cambridge University Press, 1966. Zbl0149.03003
  4. [4] B. E. J. Dahlberg, On the radial boundary values of subharmonic functions, Math. Scand. 40 (1977), 301-317. Zbl0371.31001
  5. [5] P. Fatou, Séries trigonométriques et séries de Taylor, Acta Math. 30 (1906), 335-400. Zbl37.0283.01
  6. [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. [7] J. E. Littlewood, On functions subharmonic in a circle, II, Proc. London Math. Soc. 28 (1928), 383-394. Zbl54.0516.04
  8. [8] R. Nevanlinna, Analytic Functions, Springer, 1970. 
  9. [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. [10] T. J. Ransford, On the range of an analytic multivalued function, Pacific J. Math. 123 (2) (1986), 421-439. Zbl0553.30034
  11. [11] Z. Słodkowski, Analytic set-valued functions and spectra, Math. Ann. 256 (1981), 363-386. Zbl0452.46028

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.