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Schur Parameters, Factorization and Dilation Problems
von Tiberiu ConstantinescuInhaltsverzeichnis
- 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.