Indeterminate Jacobi operators II
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915534792032256 |
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| author | Berg, Christian Szwarc, Ryszard |
| author_facet | Berg, Christian Szwarc, Ryszard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04690 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Indeterminate Jacobi operators II Berg, Christian Szwarc, Ryszard Functional Analysis Complex Variables 47B25, 47B36, 44A60 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. |
| title | Indeterminate Jacobi operators II |
| topic | Functional Analysis Complex Variables 47B25, 47B36, 44A60 |
| url | https://arxiv.org/abs/2510.04690 |