Analytic function theory for operator-valued free probability

DOI10.1515/crelle-2014-0106zbMath1381.46059arXiv1309.0877OpenAlexW2962876676MaRDI QIDQ2398717

John D. Williams

Publication date: 21 August 2017

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.0877

zbMATH Keywords

infinite divisibilityCauchy transformsVoiculescu transformoperator-valued free probability

Mathematics Subject Classification ID

Free probability and free operator algebras (46L54)

Related Items (10)

Relations between convolutions and transforms in operator-valued free probability ⋮ The royal road to automatic noncommutative real analyticity, monotonicity, and convexity ⋮ Spectral properties of polynomials in independent Wigner and deterministic matrices ⋮ Noncommutative rational Clark measures ⋮ On Semicircular Elements Induced by Connected Finite Graphs ⋮ Cauchy transforms arising from homomorphic conditional expectations parametrize noncommutative Pick functions ⋮ Subordination methods for free deconvolution ⋮ Operator-valued chordal Loewner chains and non-commutative probability ⋮ Representation of free Herglotz functions ⋮ An operad of non-commutative independences defined by trees

Cites Work

• Infinite divisibility and a non-commutative Boolean-to-free Bercovici-Pata bijection
• A general framwork for a multi-operator functional calculus
• Analytic subordination theory of operator-valued free additive convolution and the solution of a general random matrix problem
• Noncommutative rational functions, their difference-differential calculus and realizations
• Non-commutative functions and the non-commutative free Lévy-Hinčin formula
• An analogue of Hinčin's characterization of infinite divisibility for operator-valued free probability
• Gateaux differentiability and essential boundedness
• Characterization of analytic functions in Banach spaces
• Convolution powers in the operator-valued framework
• Lectures on the Combinatorics of Free Probability
• Combinatorial theory of the free product with amalgamation and operator-valued free probability theory
• On operator-valued free convolution powers
• Functions of several noncommuting variables
• Derivatives and Fréchet differentials
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