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Closable Hankel Operators and Moment Problems

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Abstract

In a paper from 2016 D. R. Yafaev considers Hankel operators associated with Hamburger moment sequences \(q_n\) and claims that the corresponding Hankel form is closable if and only if the moment sequence tends to 0. The claim is not correct, since we prove closability for any indeterminate moment sequence but also for certain determinate moment sequences corresponding to measures with finite index of determinacy. In an Erratum Yafaev (Integr Equ Oper Theory, to appear) has proved the result under quasi-analyticity assumptions, which imply that the moment sequence is determinate.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark

    Christian Berg

  2. Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384, Wrocław, Poland

    Ryszard Szwarc

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  1. Christian Berg
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  2. Ryszard Szwarc
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Correspondence to Christian Berg.

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Berg, C., Szwarc, R. Closable Hankel Operators and Moment Problems. Integr. Equ. Oper. Theory 92, 5 (2020). https://doi.org/10.1007/s00020-020-2561-z

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  • DOI: https://doi.org/10.1007/s00020-020-2561-z

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