Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-30T21:03:58.251Z Has data issue: false hasContentIssue false
  • English
  • Français

EXTENSIONS OF A THEOREM OF VALIRON

Published online by Cambridge University Press:  20 September 2006

KARL F. BARTH  and
PHILIP J. RIPPON
KARL F. BARTH
Affiliation:
Department of Mathematics, Syracuse University, Syracuse, NY 13244, [email protected]
PHILIP J. RIPPON
Affiliation:
Department of Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, United [email protected]
Get access

Abstract

A classical theorem of Valiron states that a function which is holomorphic in the unit disk, unbounded, and bounded on a spiral that accumulates at all points of the unit circle, has asymptotic value $\infty$. This property, and various other properties of such functions, are shown to hold for more general classes of functions which are bounded on a subset of the disk that has a suitably large set of nontangential limit points on the unit circle.

Keywords

30D40 (primary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 5 , October 2006 , pp. 815 - 824
Copyright
© The London Mathematical Society 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)