TY - UNPB

T1 - Noncommutative Christoffel-Darboux Kernels

AU - Belinschi, Serban T.

AU - Magron, Victor

AU - Vinnikov, Victor

PY - 2021/6/1

Y1 - 2021/6/1

N2 - 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.

AB - 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.

KW - Mathematics - Operator Algebras

KW - Mathematics - Complex Variables

KW - Mathematics - Optimization and Control

M3 - פרסום מוקדם

T3 - arXiv preprint

BT - Noncommutative Christoffel-Darboux Kernels

ER -