Schur Parameters, Factorization and Dilation Problems

Inhaltsverzeichnis

• 1 Schur Parameters and Positive Block Matrices.
• 1.1 Preliminaries.
• 1.2 Renorming Hilbert Spaces and Elementary Rotations.
• 1.3 Kolmogorov Decompositions. I.
• 1.4 Row and Column Contractions.
• 1.5 The Structure of Positive Definite Kernels.
• 1.6 Kolmogorov Decompositions. II.
• 1.7 Notes.
• 2 Models for Triangular Contractions.
• 2.1 Preliminaries.
• 2.2 The Structure of Triangular Contractions.
• 2.3 Realization of Triangular Contractions.
• 2.4 Unitary Couplings and Operator Ranges.
• 2.5 Modeling Families of Contractions.
• 2.6 Notes.
• 3 Moment Problems and Interpolation.
• 3.1 A Survey on Completion Problems.
• 3.2 Extensions of Partial Isometries.
• 3.3 Krein’s Formula.
• 3.4 Moment Problems.
• 3.5 The Commutant Lifting Method.
• 3.6 Notes.
• 4 Displacement Structures.
• 4.1 Structured Matrices.
• 4.2 Generalized Schur Algorithm.
• 4.3 Discrete Transmission-Line Models.
• 4.4 Displacement Structure and Completion Problems.
• 4.5 Other Applications.
• 4.6 Notes.
• 5 Factorization of Positive Definite Kernels.
• 5.1 Spectral Factors.
• 5.2 Examples.
• 5.3 Schur’s Algorithm, Szegö’s Theory and Spectral Factors.
• 5.4 Maximum Entropy.
• 5.5 Notes.
• 6 Nonstationary Processes.
• 6.1 Modeling Nonstationary Processes.
• 6.2 Kolmogorov-Wiener Prediction.
• 6.3 Other Prediction Problems.
• 6.4 Szegö’s Limit Theorems.
• 6.5 Notes.
• 7 Graphs and Completion Problems.
• 7.1 Preliminaries.
• 7.2 Completing Positive Partial Matrices. I.
• 7.3 Completing Positive Partial Matrices. II.
• 7.4 Completing Contractive Partial Matrices.
• 7.5 Notes.
• 8 Determinantal Formulae and Optimization.
• 8.1 Determinantal Formulae.
• 8.2 Maximum Determinant Formulae.
• 8.3 Maximum Determinant for Nonchordal Graphs.
• 8.4 Inheritance Principles.
• 8.5 Notes.
• References.