Closable Hankel operators and moment problems

2019/05/08 by Berg, Christian, Szwarc, Ryszard · 2 citations
#47A05 #47B25 #47B35 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1905.03010

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. It is also established that Yafaev's result holds if the moments satisfy \root2n\ofq_2n=o(n).

Cited by

• Indeterminate Jacobi operators II
• Inverse problem for semi-infinite Jacobi matrices and associated Hilbert spaces of analytic functions

Related

• Unbounded Hankel operators and moment problems
• Hamburger moment sequences and their moment subsequences
• Rigidity of the Hamburger and Stieltjes moment sequences
• Indeterminate Stieltjes moment problems revisited
• Positive definite Hankel matrix completions and Hamburger moment\n completions