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arXiv · 2502.04629

The Schur-Agler class in infinitely many variables

Greg Knese
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Abstract

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.

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Greg Knese. 2025-02-07. The Schur-Agler class in infinitely many variables. https://doi.org/10.4153/s0008439525100878

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