Mathematical Surveys and Monographs
Volume: 199; 2014; 183 pp; Hardcover
MSC: Primary 17; 40; 46; 47;
Print ISBN: 978-1-4704-1697-3
Product Code: SURV/199
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Electronic ISBN: 978-1-4704-2001-7
Product Code: SURV/199.E
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Foundations of Free Noncommutative Function Theory

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Dmitry S. Kaliuzhnyi-Verbovetskyi; Victor Vinnikov

In this book the authors develop a theory of free noncommutative functions, in both algebraic and analytic settings. Such functions are defined as mappings from square matrices of all sizes over a module (in particular, a vector space) to square matrices over another module, which respect the size, direct sums, and similarities of matrices. Examples include, but are not limited to, noncommutative polynomials, power series, and rational expressions.

Motivation and inspiration for using the theory of free noncommutative functions often comes from free probability. An important application area is “dimensionless” matrix inequalities; these arise, e.g., in various optimization problems of system engineering. Among other related areas are those of polynomial identities in rings, formal languages and finite automata, quasideterminants, noncommutative symmetric functions, operator spaces and operator algebras, and quantum control.

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Graduate students interested in noncommutative analysis.

Foundations of Free Noncommutative Function Theory

Base Product Code Keyword List: surv; SURV; surv/199; SURV/199; surv-199; SURV-199

Print Product Code: SURV/199

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Title (HTML): Foundations of Free Noncommutative Function Theory

Author(s) (Product display): Dmitry S. Kaliuzhnyi-Verbovetskyi; Victor Vinnikov

Affiliation(s) (HTML): Drexel University, Philadelphia, PA; Ben Gurion University of the Negev, Beer Sheva, Israel

Abstract:

Book Series Name: Mathematical Surveys and Monographs

Volume: 199

Publication Month and Year: 2014-11-19

Page Count: 183

Cover Type: Hardcover

Print ISBN-13: 978-1-4704-1697-3

Online ISBN 13: 978-1-4704-2001-7

Print ISSN: 0076-5376

Online ISSN: 0076-5376

Primary MSC: 17; 40; 46; 47

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Applied Math?: false

MAA Book?: false

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Apparel or Gift: false

SXG Subject: AA; AN; PR

Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/surv-199

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Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-2001-7&pisbn=978-1-4704-1697-3&epc=SURV/199.E&ppc=SURV/199&title=Foundations%20of%20Free%20Noncommutative%20Function%20Theory&author=Dmitry%20S.%20Kaliuzhnyi-Verbovetskyi%3B%20Victor%20Vinnikov&type=R

Readership:

Graduate students interested in noncommutative analysis.

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Cover
- Cover
Title page
- Title page
Contents
- Contents
Chapter 1. Introduction
- Chapter 1. Introduction
Chapter 2. NC functions and their difference-differential calculus
- Chapter 2. NC functions and their difference-differential calculus
Index
- Index

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Foundations of Free Noncommutative Function Theory

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Table of Contents

Foundations of Free Noncommutative Function Theory

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Cover

Title page

Contents

Chapter 1. Introduction

Chapter 2. NC functions and their difference-differential calculus

Index