Indeterminate Jacobi operators II

2025/10/06 by Christian Berg, Berg, Christian, Ryszard Szwarc +1
Computer Science · Mathematics · #44A60 #47B25 #47B36 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2510.04690

openalex publication_date 2025/10/06 · openalex created_date 2025/10/09 · openalex updated_date 2026/07/28

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 ℓ². 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.

Citations

• Indeterminate Jacobi operators
• Closable Hankel operators and moment problems

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