Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-05-18T09:49:19.065Z Has data issue: false hasContentIssue false
  • English
  • Français

Continuations of Analytic Functions of Class S and Class U

Published online by Cambridge University Press:  22 January 2016

Shinji Yamashita
Shinji Yamashita*
Affiliation:
Mathematical Institute, Tδhoku University, Sendai 980, Japan
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.

Let f be of class U in Seidel’s sense ([4, p. 32], = “inner function” in [3, p. 62]) in the open unit disk D. Then f has, by definition, the radial limit f(eiθ) of modulus one a.e. on the unit circle K. As a consequence of Smirnov’s theorem [5, p. 64] we know that the function

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 40 , December 1970 , pp. 33 - 37
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Bagemihl, F., Curvilinear cluster sets of arbitrary functions, Proc. Nat. Acad. Sci. U.S.A., 41(1955), 379–382.Google Scholar
[2] Gehring, F.W., The asymptotic values for analytic functions with bounded characteristic, Quart. J. Math. Oxford, 9(1958), 282–289.CrossRefGoogle Scholar
[3] Hoffman, K., Banach spaces of analytic functions, Englewood Cliffs, N.J., 1962.Google Scholar
[4] Noshiro, K., Cluster sets, Berlin-Göttingen-Heidelberg, 1960.CrossRefGoogle Scholar
[5] Privalov, I.I., Randeigenschaften analytischer Funktionen, Berlin, 1956.Google Scholar
[6] Rudin, W., A generalization of a theorem of Frostman, Math. Scand., 21(1967), 136–143.Google Scholar
[7] Yamashita, S., On some families of analytic functions on Riemann surfaces, Nagoya Math. J., 31(1968), 57–68.CrossRefGoogle Scholar
[8] Yamashita, S., Some remarks on analytic continuations, Túhoku Math. J., 21(1969), 328–335.Google Scholar