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EXTENSIONS OF A THEOREM OF VALIRON
Published online by Cambridge University Press: 20 September 2006
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.
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- © The London Mathematical Society 2006
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