On the growth of resolvent of Toeplitz operators
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914647869751296 |
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| author | Golinskii, Leonid Kupin, Stanislas Vishnyakova, Anna |
| author_facet | Golinskii, Leonid Kupin, Stanislas Vishnyakova, Anna |
| contents | We study the growth of the resolvent of a Toeplitz operator $T_b$, defined on the Hardy space, in terms of the distance to its spectrum $σ(T_b)$. We are primarily interested in the case when the symbol $b$ is a Laurent polynomial (\emph{i.e., } the matrix $T_b$ is banded). We show that for an arbitrary such symbol the growth of the resolvent is quadratic, and under certain additional assumption it is linear. We also prove the quadratic growth of the resolvent for a certain class of non-rational symbols. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_12095 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the growth of resolvent of Toeplitz operators Golinskii, Leonid Kupin, Stanislas Vishnyakova, Anna Spectral Theory Complex Variables 47B35, 30H10, 47G10 We study the growth of the resolvent of a Toeplitz operator $T_b$, defined on the Hardy space, in terms of the distance to its spectrum $σ(T_b)$. We are primarily interested in the case when the symbol $b$ is a Laurent polynomial (\emph{i.e., } the matrix $T_b$ is banded). We show that for an arbitrary such symbol the growth of the resolvent is quadratic, and under certain additional assumption it is linear. We also prove the quadratic growth of the resolvent for a certain class of non-rational symbols. |
| title | On the growth of resolvent of Toeplitz operators |
| topic | Spectral Theory Complex Variables 47B35, 30H10, 47G10 |
| url | https://arxiv.org/abs/2401.12095 |