Asmptotic of the eigenvalues of Toeplitz matrices with even symbol
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866918224727113728 |
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| author | Rambour, Philippe |
| author_facet | Rambour, Philippe |
| contents | In this paper we consider an interval $[θ\_{1}, θ\_{2}] \subset [0, π]$ and $f$ a differentiable, periodic and even function sufficiently smooth such that $f(θ) \in [f(θ\_{1}, f(θ\_{2})] \iff θ\in [θ\_{1}, θ\_{2}]$. Then we obtain an higher order asymptotic formula for all the eigenvalues of the Toeplitz matrix $T\_N(f)$ as $N \to + \infty$ which belong to $[f(θ\_{1}, f(θ\_{2})]$ (resp. $[f(θ\_{2}, f(θ\_1)]$). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2101_11250 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Asmptotic of the eigenvalues of Toeplitz matrices with even symbol Rambour, Philippe Classical Analysis and ODEs Operator Algebras Spectral Theory In this paper we consider an interval $[θ\_{1}, θ\_{2}] \subset [0, π]$ and $f$ a differentiable, periodic and even function sufficiently smooth such that $f(θ) \in [f(θ\_{1}, f(θ\_{2})] \iff θ\in [θ\_{1}, θ\_{2}]$. Then we obtain an higher order asymptotic formula for all the eigenvalues of the Toeplitz matrix $T\_N(f)$ as $N \to + \infty$ which belong to $[f(θ\_{1}, f(θ\_{2})]$ (resp. $[f(θ\_{2}, f(θ\_1)]$). |
| title | Asmptotic of the eigenvalues of Toeplitz matrices with even symbol |
| topic | Classical Analysis and ODEs Operator Algebras Spectral Theory |
| url | https://arxiv.org/abs/2101.11250 |