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The Schur–Agler class in infinitely many variables
- Part of
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- Journal:
- Canadian Mathematical Bulletin , First View
- Published online by Cambridge University Press:
- 14 July 2025, pp. 1-19
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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.
