Self-adjoint operators associated with Hankel moment matrices
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Self-adjoint operators associated with Hankel moment matrices. / Berg, Christian; Szwarc, Ryszard.
In: Journal of Functional Analysis, Vol. 283, No. 10, 109674, 2022, p. 1-29.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Self-adjoint operators associated with Hankel moment matrices
AU - Berg, Christian
AU - Szwarc, Ryszard
N1 - Publisher Copyright: © 2022 Elsevier Inc.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Hankel operators
KW - Moment problems
UR - http://www.scopus.com/inward/record.url?scp=85135814797&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2022.109674
DO - 10.1016/j.jfa.2022.109674
M3 - Journal article
AN - SCOPUS:85135814797
VL - 283
SP - 1
EP - 29
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 10
M1 - 109674
ER -
ID: 317813027