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Article Dans Une Revue Transactions of the American Mathematical Society Année : 2023

Noncommutative Christoffel-Darboux Kernels

Résumé

We introduce from an analytic perspective Christoffel-Darboux kernels associated to bounded, tracial noncommutative distributions. We show that properly normalized traces, respectively norms, of evaluations of such kernels on finite dimensional matrices yield classical plurisubharmonic functions as the degree tends to infinity, and show that they are comparable to certain noncommutative versions of the Siciak extremal function. We prove estimates for Siciak functions associated to free products of distributions, and use the classical theory of plurisubharmonic functions in order to propose a notion of support for noncommutative distributions. We conclude with some conjectures and numerical experiments.

Dates et versions

hal-03433869 , version 1 (18-11-2021)

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Serban Belinschi, Victor Magron, Victor Vinnikov. Noncommutative Christoffel-Darboux Kernels. Transactions of the American Mathematical Society, 2023, 376, pp.181-230. ⟨10.1090/tran/8648⟩. ⟨hal-03433869⟩
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