Free analysis questions I: duality transform for the coalgebra of ∂X:B

By D. Voiculescu. 2004

113 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f37b4956a35e04b4d7b609fed9dc39f77d794410

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In Statistics and Probability

Citations in the corpus

Global Holomorphic Functions in Several Noncommuting Variables (2015, unknown): “This has been done in a variety of ways: by Taylor [23], in the context of the functional calculus for non-commuting operators; Voiculescu [24, 25], in the context of free probability; Popescu [18, 19, 20, 21], in the context of extending classical function theory to d-tuples Partially supported by ”
Foundations of Free Noncommutative Function Theory (2012, background): “[106] D.-V. Voiculescu.”
Interpolation and transfer-function realization for the noncommutative Schur-Agler class (2016, background): “s given locally by a power series representation of the sort in (1.7). Closely related approaches to and results on such a “free noncommutative function theory” can be found in the work of Voiculescu [81, 82] and Helton-Klep-McCullough [45, 46, 47]. The purpose of the present paper is to extend the ”
Free analysis questions II: The Grassmannian completion and the series expansions at the origin (2008, methodology): “One reason is the duality transform for the coalgebra of the free di¤erence quotient ([16] see also [15]).”
Noncommutative reproducing kernel Hilbert spaces (2016, background): “ Taylor [47] (see also [48]) as a setting for the study of a functional calculus for tuples of freely noncommuting matrix variables, and independently in the work of Voiculescu and collaborators (see [49, 50]) in the context of the needs of a free-probability theory, as well as in the work of Helton”
Free Probability and Random Matrices (2014, methodology): “Free analysis was started by Voiculescu in the context of free probability around 2000 [48, 49, 50]; it builds on the seminal work of J.L. Taylor [39].”
Every convex free basic semi-algebraic set has an LMI representation (2012, background): “because the matrices involved are symmetric, a property not generally preserved under similarity, Dp is not a free set in the sense of Voiculescu [Voi] [Voi05].”