On the type of ill-posedness of generalized Hilbert matrices and related operators
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914671193227264 |
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| author | Kindermann, Stefan |
| author_facet | Kindermann, Stefan |
| contents | We consider infinite-dimensional generalized Hilbert matrices of the form $H_{i,j} = \frac{d_i d_j}{x_i + x_j}$, where $d_i$ are nonnegative weights and $x_i$ are pairwise disjoint positive numbers. We state sufficient and, for monotonically rearrangeable $x_i$, also necessary conditions for $d_i$, $x_i$ such that the induced operator from $\ell^2 \to \ell^2$ and related operators are well-defined, bounded, or compact. Furthermore, we give conditions, when this operator is injective and ill-posed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05503 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the type of ill-posedness of generalized Hilbert matrices and related operators Kindermann, Stefan Functional Analysis We consider infinite-dimensional generalized Hilbert matrices of the form $H_{i,j} = \frac{d_i d_j}{x_i + x_j}$, where $d_i$ are nonnegative weights and $x_i$ are pairwise disjoint positive numbers. We state sufficient and, for monotonically rearrangeable $x_i$, also necessary conditions for $d_i$, $x_i$ such that the induced operator from $\ell^2 \to \ell^2$ and related operators are well-defined, bounded, or compact. Furthermore, we give conditions, when this operator is injective and ill-posed. |
| title | On the type of ill-posedness of generalized Hilbert matrices and related operators |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2402.05503 |