On local non-tangential growth of the resolvent of a banded Toeplitz operator
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908388004200448 |
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| author | Golinskii, L. Kupin, S. |
| author_facet | Golinskii, L. Kupin, S. |
| contents | We study the growth of the resolvent of a Hardy--Toeplitz operator $T_b$ with a Laurent polynomial symbol (\emph{i.e., } the matrix $T_b$ is banded), at the neighborhood of a point $w_0\in\partial(σ(T_b))$ on the boundary of its spectrum. We show that such growth is inverse linear in some non-tangential domains at the vertex $w_0$, provided that $w_0$ does not belong to a certain finite set on the complex plane. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_00584 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On local non-tangential growth of the resolvent of a banded Toeplitz operator Golinskii, L. Kupin, S. Spectral Theory Primary: 47B35, Secondary: 30H10, 47G10 We study the growth of the resolvent of a Hardy--Toeplitz operator $T_b$ with a Laurent polynomial symbol (\emph{i.e., } the matrix $T_b$ is banded), at the neighborhood of a point $w_0\in\partial(σ(T_b))$ on the boundary of its spectrum. We show that such growth is inverse linear in some non-tangential domains at the vertex $w_0$, provided that $w_0$ does not belong to a certain finite set on the complex plane. |
| title | On local non-tangential growth of the resolvent of a banded Toeplitz operator |
| topic | Spectral Theory Primary: 47B35, Secondary: 30H10, 47G10 |
| url | https://arxiv.org/abs/2506.00584 |