Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2511.19247 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908672019398656 |
|---|---|
| author | Zalar, Aljaž Zobovič, Igor |
| author_facet | Zalar, Aljaž Zobovič, Igor |
| contents | Let $L$ be a linear operator on univariate polynomials of bounded degree taking values in real symmetric matrices, whose moment matrix is positive semidefinite. Assume that $L$ admits a positive matrix-valued representing measure $μ$. Any finitely atomic representing measure with the smallest sum of the ranks of the matricial masses is called minimal. In this paper, we characterize the existence of a minimal representing measure that contains a prescribed atom with a prescribed rank of the corresponding mass, thereby generalizing our recent result, which addresses the same problem in the case where the moment matrix is positive definite. As a corollary, we obtain a constructive, linear-algebraic proof of the strong truncated Hamburger matrix moment problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19247 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matricial Gaussian quadrature rules: singular case Zalar, Aljaž Zobovič, Igor Functional Analysis Algebraic Geometry Primary 65D32, 47A57, 47A20, 44A60, Secondary 15A04, 47N40 Let $L$ be a linear operator on univariate polynomials of bounded degree taking values in real symmetric matrices, whose moment matrix is positive semidefinite. Assume that $L$ admits a positive matrix-valued representing measure $μ$. Any finitely atomic representing measure with the smallest sum of the ranks of the matricial masses is called minimal. In this paper, we characterize the existence of a minimal representing measure that contains a prescribed atom with a prescribed rank of the corresponding mass, thereby generalizing our recent result, which addresses the same problem in the case where the moment matrix is positive definite. As a corollary, we obtain a constructive, linear-algebraic proof of the strong truncated Hamburger matrix moment problem. |
| title | Matricial Gaussian quadrature rules: singular case |
| topic | Functional Analysis Algebraic Geometry Primary 65D32, 47A57, 47A20, 44A60, Secondary 15A04, 47N40 |
| url | https://arxiv.org/abs/2511.19247 |