Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



One-sided cluster-set theory in a polydisc

Authors: C. L. Childress and G. L. Csordas
Journal: Proc. Amer. Math. Soc. 77 (1979), 41-47
MSC: Primary 30D40; Secondary 32A40
MathSciNet review: 539628
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we develop a technique which reduces the investigation of the boundary behavior of a single function f in $ {H^\infty }({U^n}),n > 1$, to the study of the cluster sets of a sequence of functions in $ {H^\infty }(U)$. We also demonstrate the significance and usefulness of one-sided cluster-set theory.

References [Enhancements On Off] (What's this?)

  • [1] R. H. Cameron and D. A. Storvick, A Lindelöf theorem and analytic continuation for functions of several variables, with an application to the Feynman integral, Proc. Sympos. Pure Math., vol. 11, Amer. Math. Soc., Providence, R. I., 1968, pp. 149-158. MR 0237815 (38:6096)
  • [2] C. L. Childress and G. L. Csordas, The Iversen theorem in a polydisc, Math. Scand. 42 (1978), 64-70. MR 0486594 (58:6314)
  • [3] -, The theory of cluster sets in the unit polydisc, Festschrift für Rolf Nevanlinna, Silivri (to appear).
  • [4] E. F. Collingwood and A. J. Lohwater, The theory of cluster sets, Cambridge Tracts in Math. Physics, no. 56, Cambridge Univ. Press, Cambridge, 1966. MR 0231999 (38:325)
  • [5] J. L. Doob, The boundary values of analytic functions, Trans. Amer. Math. Soc. 35 (1933), 418-451. MR 1501694
  • [6] -, One-sided cluster-value theorems, Proc. London Math. Soc. (3) 13 (1963), 461-470. MR 0166365 (29:3642)
  • [7] F. W. Gehring and A. J. Lohwater, On the Lindelöf theorem, Math. Nachr. 19 (1958), 165-170. MR 0105506 (21:4246)
  • [8] W. Gross, Zum Verhalten der konformen Abbildung am Rande, Math. Z. 3 (1919), 43-64. MR 1544335
  • [9] F. Iversen, Sur quelques propriétés des fonctions monogènes au voisinage d'un point singulier, Öfvers. Finska Vetensk. Soc. Forh. 58A, no. 25 (1915/16), 1-16.
  • [10] E. Lindelöf, Sur un principe général de l'analyse et ses applications à la theorie de la représentation conforme, Acta Soc. Sci. Fenn. 46, no. 4 (1915), 1-35.
  • [11] A. J. Lohwater, The boundary behaviour of analytic functions, Mathematical Analysis, Vol. 10, Akad. Nauk SSP Vsesojuz. Inst. Naučn. i Tehn. Informacii, Moscow, 1973. (Russian) MR 0399467 (53:3311)
  • [12] G. T. Whyburn, Analytic topology, Amer. Math. Soc. Colloq. Publ., vol. 28, Amer. Math. Soc., Providence, R. I., 1967. MR 0182943 (32:425)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30D40, 32A40

Retrieve articles in all journals with MSC: 30D40, 32A40

Additional Information

Keywords: One-sided cluster sets, angular and principal cluster sets, the Iversen-Doob Theorem, the Lindelöf Theorem, the Gross Cluster-Value Theorem, the Gehring-Lohwater Theorem
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society