Self-adjoint operators associated with Hankel moment matrices
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In a paper from 2016 D. R. Yafaev initiated a study of closable Hankel forms associated with the moments (mn) of a positive measure with infinite support on the real line. If mn=o(1) Yafaev characterized the closure of the form based on earlier work on quasi-Carleman operators. We give a new proof of the description of the closure based entirely on moment considerations. The main purpose of the present paper is a description of the self-adjoint Hankel operators associated with closed Hankel forms in the Hilbert space of square summable sequences. We do this not only in the case mn=o(1) studied by Yafaev but also in two other cases, where the Hankel form is closable, namely if the moment sequence is indeterminate or if the moment sequence is determinate with finite index of determinacy.
Original language | English |
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Article number | 109674 |
Journal | Journal of Functional Analysis |
Volume | 283 |
Issue number | 10 |
Pages (from-to) | 1-29 |
ISSN | 0022-1236 |
DOIs | |
Publication status | Published - 2022 |
Bibliographical note
Publisher Copyright:
© 2022 Elsevier Inc.
- Hankel operators, Moment problems
Research areas
ID: 317813027