Global Holomorphic Functions in Several Noncommuting Variables

By Jim Agler, John E. McCarthy. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2015

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Noncommutative reproducing kernel Hilbert spaces (2016, methodology): “In our followup paper [13] we use various parts of the material in the present paper to develop further the work of Agler-McCarthy [2, 3] on noncommutative Pick interpolation and transfer-function realization and introduce a free noncommutative version of “complete Pick kernel”(see [1] for the class”
Algebras of bounded noncommutative analytic functions on subvarieties of the noncommutative unit ball (2017, background): “Recently, many works laid out the foundations of noncommutative free analysis, such as [44], [3,4,6] and [67].”
Interpolation and transfer-function realization for the noncommutative Schur-Agler class (2016, methodology): “el Γ: Ω×Ω → L(S,L(Y))nc so that P⊗IY −S(Z)(P⊗IU)S(W)∗ (3.9) = Γ(Z,W)((P⊗IS) −Q(Z)(P⊗IR)Q(W)∗). (3.10) (3) Shas a transfer-function realization as in (3.7). It has been observed by Agler-McCarthy (see [6]) that Corollary 3.2 can be used to prove nc analogues of the Oka-Weil approximation theory for h”