Serban T. Belinschi, Victor Magron, Victor Vinnikov

Research output: Contribution to journalArticlepeer-review


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
Pages (from-to)181-230
Number of pages50
JournalTransactions of the American Mathematical Society
Issue number1
StatePublished - 1 Jan 2023


  • Bernstein-Markov property
  • Christoffel-Darboux kernels
  • GNS construction
  • Noncommutative polynomials
  • semialgebraic set
  • semidefinite programming
  • trace optimization

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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