An extremal problem for analytic functions with prescribed zeros and th derivative in

Authors:
A. Horwitz and D. J. Newman

Journal:
Trans. Amer. Math. Soc. **295** (1986), 699-713

MSC:
Primary 30C75; Secondary 30D50

DOI:
https://doi.org/10.1090/S0002-9947-1986-0833704-4

MathSciNet review:
833704

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Abstract: Let be points in the unit disc . Suppose is analytic in , (multiplicities included), and . Then we prove that for all , where and is a Blaschke product of order . We extend this result in a natural way to convex domains with analytic boundary. For not convex we show that there is no extremal function .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1986-0833704-4

Article copyright:
© Copyright 1986
American Mathematical Society