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Computing Interpolating Sequences

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Abstract

Naftalevič’s Theorem states that, given a Blaschke sequence, it is possible to modify the arguments of its terms so as to obtain an interpolating sequence. We prove a computable version of this theorem in that it possible, given a Blaschke sequence, to computably modify the arguments of its terms so as to obtain an interpolating sequence. Using this result, we produce a computable, interpolating Blaschke sequence that does not define a computable Blaschke product. This answers a question posed by Matheson and McNicholl in a recent paper. We use Type-Two Effectivity as our foundation.

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Authors and Affiliations

  1. Department of Mathematics, Lamar University, Beaumont, TX, 77710, USA

    Valentin V. Andreev & Timothy H. McNicholl

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  1. Valentin V. Andreev
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  2. Timothy H. McNicholl
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Correspondence to Timothy H. McNicholl.

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Andreev, V.V., McNicholl, T.H. Computing Interpolating Sequences. Theory Comput Syst 46, 340–350 (2010). https://doi.org/10.1007/s00224-008-9140-z

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  • DOI: https://doi.org/10.1007/s00224-008-9140-z

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