Generalised eigenvector expansion of infinite Toeplitz matrices with absolutely/completely monotone entries
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866916073972957184 |
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| author | Kwaśnicki, Mateusz Wszoła, Jacek |
| author_facet | Kwaśnicki, Mateusz Wszoła, Jacek |
| contents | We study the spectral theory of infinite Toeplitz matrices $T = (a_{k - l})$ under the assumption that $(a_k)$ and $(a_{-k})$ are completely monotone sequences. We derive expressions for generalised eigenvectors and prove a generalised eigenvector expansion of $T$. Even if the matrix $T$ is not normal, our expressions involve only eigenvalues and eigenvectors with real entries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01986 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalised eigenvector expansion of infinite Toeplitz matrices with absolutely/completely monotone entries Kwaśnicki, Mateusz Wszoła, Jacek Spectral Theory Probability We study the spectral theory of infinite Toeplitz matrices $T = (a_{k - l})$ under the assumption that $(a_k)$ and $(a_{-k})$ are completely monotone sequences. We derive expressions for generalised eigenvectors and prove a generalised eigenvector expansion of $T$. Even if the matrix $T$ is not normal, our expressions involve only eigenvalues and eigenvectors with real entries. |
| title | Generalised eigenvector expansion of infinite Toeplitz matrices with absolutely/completely monotone entries |
| topic | Spectral Theory Probability |
| url | https://arxiv.org/abs/2606.01986 |