Foundations of Free Noncommutative Function Theory
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A01=Dmitry S. Kaliuzhnyi-Verbovetskyi
A01=Victor Vinnikov
Author_Dmitry S. Kaliuzhnyi-Verbovetskyi
Author_Victor Vinnikov
Category=PBF
Category=PBH
Category=PBMW
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Product details
- ISBN 9781470416973
- Weight: 456g
- Dimensions: 178 x 254mm
- Publication Date: 30 Dec 2014
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Hardback
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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.
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.
