Journal of Operator Theory

Volume 93, Issue 1, Winter 2025 pp. 123-145.

Indeterminate Jacobi operators

Authors: Christian Berg (1), Ryszard Szwarc (2)
Author institution: (1) Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Universitetsparken 5, DK-2100, Denmark
(2) Institute of Mathematics, University of Wroc{\l}aw, Wro\-c{\l}aw, pl.\ Grunwaldzki 2/4, 50-384 Poland

Summary: We consider the Jacobi operator $(T,D(T))$ associated with an indeterminate Hamburger moment problem. For a complex number $z$ let $\mathfrak{p}_z, \mathfrak{q}_z$ denote the square summable sequences $(p_n(z))$ and $(q_n(z))$ corresponding to the orthonormal polynomials $p_n$ and polynomials $q_n$ of the second kind. We determine whether linear combinations of $\mathfrak{p}_u, \mathfrak{p}_v,\mathfrak{q}_u,\mathfrak{q}_v$ for complex $u,v$ belong to $D(T)$ or to the domain of the self-adjoint extensions of $T$ in $\ell^2$ . The results depend on the four Nevanlinna functions of two variables associated with the moment problem.

DOI: http://dx.doi.org/10.7900/jot.2023ian02.2404
Keywords: Jacobi matrices and operators, indeterminate moment problems

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