
Foundations of Free Noncommutative Function Theory
American Mathematical Society (Publisher)
Will be published approx. on 30. December 2014
Book
Hardback
183 pages
978-1-4704-1697-3 (ISBN)
Description
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, quantum control.
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, quantum control.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
Weight
456 gr
ISBN-13
978-1-4704-1697-3 (9781470416973)
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Schweitzer Classification
Persons
Dmitry S. Kaliuzhnyi-Verbovetskyi, Drexel University, Philadelphia, PA, USA.
Victor Vinnikov, Ben Gurion University of the Negev, Beer Sheva, Israel.
Victor Vinnikov, Ben Gurion University of the Negev, Beer Sheva, Israel.
Content
Introduction
NC functions and their difference-differential calculus
Higher order nc functions and their difference-differential calculus
The Taylor-Taylor formula
NC functions on nilpotent matrices
NC polynomials vs. polynomials in matrix entries
NC analyticity and convergence of TT series
Convergence of nc power series
Direct summands extensions of nc sets and nc functions (Some) earlier work on nc functions
Similarity invariant envelopes and extension of nc functions
Bibliography
Index
NC functions and their difference-differential calculus
Higher order nc functions and their difference-differential calculus
The Taylor-Taylor formula
NC functions on nilpotent matrices
NC polynomials vs. polynomials in matrix entries
NC analyticity and convergence of TT series
Convergence of nc power series
Direct summands extensions of nc sets and nc functions (Some) earlier work on nc functions
Similarity invariant envelopes and extension of nc functions
Bibliography
Index