Extremal interpolatory functions in 𝐻^{∞}

Øyma, Knut

doi:10.1090/S0002-9939-1977-0447586-6

Extremal interpolatory functions in $H^{\infty }$
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by Knut Øyma

Proc. Amer. Math. Soc. 64 (1977), 272-276

DOI: https://doi.org/10.1090/S0002-9939-1977-0447586-6

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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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