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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]
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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

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