On the Growth of the Resolvent of a Toeplitz Operator
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 $\sigma(T_b)$. We are primarily interested in the case when the symbol $b$ is a Laurent polynomial (i.e., the matrix $T_b$ is banded). We show that for an arbitrar...
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| Date: | 2024 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2024
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| Subjects: | |
| Online Access: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1086 |
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| Journal Title: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Summary: | 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 $\sigma(T_b)$. We are primarily interested in the case when the symbol $b$ is a Laurent polynomial (i.e., the matrix $T_b$ is banded). We show that for an arbitrary such symbol the growth of the resolvent is quadratic (3.1), and under certain additional assumption it is linear (2.1). We also prove the quadratic growth of the resolvent for a certain class of non-rational symbols.
Mathematical Subject Classification 2020: 47B35, 30H10, 47G10 |
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