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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Extremal interpolatory functions in $H^{\infty }$


Author: Knut Øyma
Journal: Proc. Amer. Math. Soc. 64 (1977), 272-276
MSC: Primary 30A80
DOI: https://doi.org/10.1090/S0002-9939-1977-0447586-6
MathSciNet review: 0447586
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Abstract: Let a Blaschke sequence $\{ {z_n}\}$ and a bounded sequence $\{ {w_n}\}$ be given. If we can find an f in ${H^\infty }$ such that $f({z_n}) = {w_n}$ we may assume that $\left \| f \right \|$ is minimal. Such an f need not be unique, but a sufficient condition for uniqueness is given. Properties of f in the case of uniqueness are studied.


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Article copyright: © Copyright 1977 American Mathematical Society