Indeterminate Jacobi operators II
Functional Analysis
2025-10-07 v1 Complex Variables
Abstract
We consider the Jacobi operator (T,D(T)) associated with an indeterminate Hamburger moment problem, and present countable subsets S of the domain D(T) such that span(S) is dense in \ell^2. As an example we have S={(p_n(u))+B(u)(p_n(0)):D(u)=0}, where (p_n) denotes the orthonormal polynomials of the moment problem and B,D are two of the Nevanlinna functions. It is also proved that sets like S are optimal in the sense that if one vector is removed, then the span is no longer dense.
Cite
@article{arxiv.2510.04690,
title = {Indeterminate Jacobi operators II},
author = {Christian Berg and Ryszard Szwarc},
journal= {arXiv preprint arXiv:2510.04690},
year = {2025}
}
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12 pages