Free interpolation by nonvanishing analytic functions

Konstantin Dyakonov, Artur Nicolau

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8 Citations (Scopus)

Abstract

We are concerned with interpolation problems in H∞ where the values prescribed and the function to be found are both zero-free. More precisely, given a sequence {zj} in the unit disk, we ask whether there exists a nontrivial minorant {ej} (i.e., a sequence of positive numbers bounded by 1 and tending to 0) such that every interpolation problem f(zj) = aj has a nonvanishing solution f ∈ H∞ whenever 1 ≥ |aj| ≥ ej for all j. The sequences {zj} with this property are completely characterized. Namely, we identify them as "thin" sequences, a class that arose earlier in Wolff's work on free interpolation in H∞ ∩ VMO. © 2007 American Mathematical Society.
Original languageEnglish
Pages (from-to)4449-4465
JournalTransactions of the American Mathematical Society
Volume359
Issue number9
DOIs
Publication statusPublished - 1 Dec 2007

Keywords

  • Nonvanishing analytic functions
  • Thin interpolating sequences

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    Dyakonov, K., & Nicolau, A. (2007). Free interpolation by nonvanishing analytic functions. Transactions of the American Mathematical Society, 359(9), 4449-4465. https://doi.org/10.1090/S0002-9947-07-04186-4