Nondiscriminating sets for 𝐻^{∞}

Marshall, Donald E.; Stray, Arne; Sundberg, Carl

doi:10.1090/S0002-9939-1982-0667286-9

Nondiscriminating sets for $H^{\infty }$
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by Donald E. Marshall, Arne Stray and Carl Sundberg PDF

Proc. Amer. Math. Soc. 86 (1982), 267-272 Request permission

Abstract:

We characterize the subsets $S$ of the unit disk $D$ with the property that any function defined on $S$ that has a bounded harmonic extension to $D$, must also have a bounded analytic extension to $D$.

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