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Omitted rays and wedges of fractional Cauchy transforms
Part of:
Spaces and algebras of analytic functions
Miscellaneous topics of analysis in the complex domain
Published online by Cambridge University Press: 09 April 2009
Abstract
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For α > 0 let α denote the set of functions which can be expressed where μ is a complex-valued Borel measure on the unit circle. We show that if f is an analytic function in Δ = {z ∈ : |z| < 1} and there are two nonparallel rays in /f(Δ) which do not meet, then f ∈ α where απ denotes the largest of the two angles determined by the rays. Also if the range of a function analytic in Δ is contained in an angular wedge of opening απ and 1 < α < 2, then f ∈ α.
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- Copyright © Australian Mathematical Society 2006
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