The Schur-Agler class in infinitely many variables
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911053278871552 |
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| author | Knese, Greg |
| author_facet | Knese, Greg |
| contents | We define the Schur-Agler class in infinite variables to consist of functions whose restrictions to finite dimensional polydisks belong to the Schur-Agler class. We show that a natural generalization of an Agler decomposition holds and the functions possess transfer function realizations that allow us to extend the functions to the unit ball of $\ell^\infty$. We also give a Pick interpolation type theorem which displays a subtle difference with finitely many variables. Finally, we make a brief connection to Dirichlet series derived from the Schur-Agler class in infinite variables via the Bohr correspondence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04629 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Schur-Agler class in infinitely many variables Knese, Greg Functional Analysis Complex Variables 47A48, 47A13, 47A57, 46E50, 30B50, 32A38, 46G20, 32E30 We define the Schur-Agler class in infinite variables to consist of functions whose restrictions to finite dimensional polydisks belong to the Schur-Agler class. We show that a natural generalization of an Agler decomposition holds and the functions possess transfer function realizations that allow us to extend the functions to the unit ball of $\ell^\infty$. We also give a Pick interpolation type theorem which displays a subtle difference with finitely many variables. Finally, we make a brief connection to Dirichlet series derived from the Schur-Agler class in infinite variables via the Bohr correspondence. |
| title | The Schur-Agler class in infinitely many variables |
| topic | Functional Analysis Complex Variables 47A48, 47A13, 47A57, 46E50, 30B50, 32A38, 46G20, 32E30 |
| url | https://arxiv.org/abs/2502.04629 |