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Univalent functions of fast growth with gap power series

Published online by Cambridge University Press:  01 November 1999

ALEXANDRE EREMENKO  and
WALTER HAYMAN
ALEXANDRE EREMENKO
Affiliation:
Purdue University, West Lafayette, IN 47907, U.S.A. e-mail: [email protected]
WALTER HAYMAN
Affiliation:
Imperial College, London SW7 2BZ
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Abstract

We construct univalent functions in the unit disc, whose coefficient sequences (an) have arbitrarily long intervals of zeros and at the same time arbitrarily long intervals where [mid ]an[mid ] > nεn holds, (εn) being an arbitrary prescribed sequence of positive numbers tending to zero. Furthermore we show that the initial interval of coefficients of such a function can be prescribed to be any interior point of the coefficient region.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 127 , Issue 3 , November 1999 , pp. 525 - 532
Copyright
© The Cambridge Philosophical Society 1999

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