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A gap condition for the zeroes of certain polynomials in Kaplan classes K(α, β)

Part of: Geometric function theory

Published online by Cambridge University Press:  26 February 2010

Massoud Jahangiri
Massoud Jahangiri
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506, U.S.A.
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Extract

For α≥0 and β≥0 we denote by K (α, β) the Kaplan classes of functions f analytic and non-zero in the open unit disk U = {z: |z| < 1} such that f ∈ K(α, β), if, and only if, for θ1 < θ2 < θ1 + 2π and 0 < r < 1,

Where

MSC classification

Secondary: 30C15: Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral)
Type
Research Article
Information
Mathematika , Volume 34 , Issue 1 , June 1987 , pp. 53 - 63
Copyright
Copyright © University College London 1987

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References

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