Analytic Schur multipliers
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915349981560832 |
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| author | Aleksandrov, Aleksei Peller, Vladimir |
| author_facet | Aleksandrov, Aleksei Peller, Vladimir |
| contents | We study in this paper analytic Schur multipliers on ${\Bbb C}_+^2$ and ${\Bbb D}^2$, i.e. Schur multipliers on ${\Bbb R}^2$ and ${\Bbb T}^2$ that are boundary-value functions of functions analytic in ${\Bbb C}_+^2$ and ${\Bbb D}^2$. Such Schur multipliers are important when studying properties of functions of maximal dissipative operators and contractions under perturbation. We show that if the boundary-value function of a Schur multiplier has certain regularity properties, then it can be represented as an element of the Haagerup tensor product of spaces of analytic functions with similar regularity properties. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_15173 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analytic Schur multipliers Aleksandrov, Aleksei Peller, Vladimir Functional Analysis Classical Analysis and ODEs Complex Variables Spectral Theory 47A55, 47B10, 47A60, 47B44 We study in this paper analytic Schur multipliers on ${\Bbb C}_+^2$ and ${\Bbb D}^2$, i.e. Schur multipliers on ${\Bbb R}^2$ and ${\Bbb T}^2$ that are boundary-value functions of functions analytic in ${\Bbb C}_+^2$ and ${\Bbb D}^2$. Such Schur multipliers are important when studying properties of functions of maximal dissipative operators and contractions under perturbation. We show that if the boundary-value function of a Schur multiplier has certain regularity properties, then it can be represented as an element of the Haagerup tensor product of spaces of analytic functions with similar regularity properties. |
| title | Analytic Schur multipliers |
| topic | Functional Analysis Classical Analysis and ODEs Complex Variables Spectral Theory 47A55, 47B10, 47A60, 47B44 |
| url | https://arxiv.org/abs/2506.15173 |