Noncommutative Christoffel-Darboux Kernels

Serban T. Belinschi, Victor Magron, Victor Vinnikov

Research output: Working paper/PreprintPreprint

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Abstract

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.
Original languageEnglish GB
StatePublished - 1 Jun 2021

Publication series

NamearXiv preprint

Keywords

  • Mathematics - Operator Algebras
  • Mathematics - Complex Variables
  • Mathematics - Optimization and Control

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