Entropy and Multivariable Interpolation.

Intro -- Contents -- Introduction -- Chapter 1. Operators on Fock Spaces and their Entropy -- 1.1. Entropy and spectral factorization for multi-Toeplitz operators -- 1.2. Operators on Fock spaces and factorizations -- 1.3. Prediction entropy for positive definite multi-Toeplitz kernels on free semigroups -- 1.4. Extreme points of the unit ball of F[sup(∞)][sub(n)] -- Chapter 2. Noncommutative Commutant Lifting Theorem: Geometric Structure and Maximal Entropy Solution -- 2.1. Multivariate intertwining liftings and geometric structure -- 2.2. Central lifting in several variables and geometric characterizations -- 2.3. A maximum principle for the noncommutative commutant lifting theorem -- 2.4. A permanence principle for the central intertwining lifting -- 2.5. Quasi outer spectral factorizations -- 2.6. Noncommutative commutant lifting theorem and the maximal entropy solution -- Chapter 3. Maximal Entropy Interpolation Problems in Several Variables -- 3.1. Maximal entropy solution for the Sarason interpolation problem for analytic Toeplitz algebras -- 3.2. Maximal entropy solution for the Caratheodory-Schur interpolation problem for analytic Toeplitz algebras -- 3.3. Maximal entropy solution for the Nevanlinna-Pick interpolation problem with operatorial argument in several variables -- 3.4. Maximal entropy interpolation on the unit ball of C[sup(n)] -- Bibliography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.