Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-05T09:07:02.005Z Has data issue: false hasContentIssue false
  • English
  • Français

Horocyclic Cluster Sets of Functions Defined in the Unit Disc

Published online by Cambridge University Press:  22 January 2016

Stephen Dragosh
Stephen Dragosh*
Affiliation:
Michigan State University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper contains in part the author’s Ph.D. dissertation written under the supervision of Professor F. Bagemihl at the University of Wisconsin-Milwaukee. This research was supported by grants from the National Science Foundation and the University of Wisconsin Graduate School.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 35 , July 1969 , pp. 53 - 82
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1969

References

[1] Bagemihl, F., Curvilinear cluster sets of arbitrary functions, Proc. Nat. Acad. Sci., 41 (1955), 379–382.CrossRefGoogle ScholarPubMed
[2] Bagemihl, F., Some approximation theorems for normal functions, Ann. Acad. Sci. Fennicae AI 335 (1963), 1–5.Google Scholar
[3] Bagemihl, F., Horocyclic boundary properties of meromorphic functions, Ann. Acad. Sci. Fennicae Al 385 (1966), 1–18.Google Scholar
[4] Bagemihl, F. and Seidel, W., Some boundary properties of analytic functions, Math. Z. 61 (1954), 186–199.Google Scholar
[5] Bagemihl, F. and Seidel, W., Sequential and continuous limits of meromorphic functions, Ann. Acad. Sci. Fennicae AI 280 (1960), 1–17.Google Scholar
[6] Carathéodory, C., Theory of Functions, Vol. II, 2nd ed., Chelsea Publishing Co., New York, 1960.Google Scholar
[7] Collingwood, E.F., On sets of maximum indetermination of analytic functions, Math. Z. 67 (1957), 377–396.CrossRefGoogle Scholar
[8] Collingwood, E.F., Cluster sets of arbitrary functions, Proc. Nat. Acad. Sci. 46 (1960), 1236–1242.Google Scholar
[9] Collingwood, E.F. and Lohwater, A.J., The Theory of Cluster Sets, Cambridge Tracts in Mathematics and Mathematical Physics, No. 56, Cambridge Univ. Press, New York, 1966.Google Scholar
[10] Dragosh, S., Horocyclic boundary properties of meromorphic functions, J. d’Analyse Math, (to appear).Google Scholar
[11] Fatou, P., Séries trigonométriques et séries de Taylor, Acta Math. 30 (1906), 335–400.Google Scholar
[12] Hobson, E.W., The Theory of Functions of a Real Variable, Vol. I, 3rd ed., Harren Press, Wash., D.C., 1950.Google Scholar
[13] Jenkins, J.A., On a problem of Lusin, Mich. Math. J. 3 (1955–1956), 187–189.Google Scholar
[14] Lavrentieff, M., On certain properties of univalent functions (in Russian), Mat. Sbornik 43 (1936), 815–844, (French Summary) 845–846.Google Scholar
[15] Lehto, O. and Virtanen, K.I., Boundary behaviour and normal meromorphic functions, Acta Math. 97 (1957), 47–65.Google Scholar
[16] Littlewood, J.E., Mathematical Notes (4): On a theorem of Fatou, J. London Math. Soc. 2 (1927), 172–176.Google Scholar
[17] Lohwater, A.J. and Piranian, G., The boundary behavior of functions analytic in a disk, Ann. Acad. Sci. Fennicae AI 239 (1957), 1–17.Google Scholar
[18] Meier, K., Über die Randwerte der meromorphen Funktionen, Math. Annalen 142 (1961), 328–344.Google Scholar
[19] Montel, P., Leçons sur les familles normales de fonctions analytiques et leurs applications, Paris, 1927.Google Scholar
[20] Noshiro, K., Contributions to the theory of meromorphic functions in the unit circle, J. Fac. Sci. Hokkaido Imperial Univ. 7 (1939), 149–159.Google Scholar
[21] Noshiro, K., Cluster Sets, Berlin, 1960.CrossRefGoogle Scholar
[22] Plessner, A.I., Über das Verhalten analytischer Funktionen am Rande ihres Definitionsbereiches, J. reine angew. Math. 158 (1927), 219–227.Google Scholar
[23] Priwalow, I.I., Randeigenschaften analytischer Funktionen, Berlin, 1956.Google Scholar
[24] Riesz, F., Über die Randwerte einer analytischen Funktion, Math. Z. 18 (1923), 87–95.Google Scholar