Schur Parameters, Factorization and Dilation Problems von Tiberiu Constantinescu | ISBN 9783034899109

Schur Parameters, Factorization and Dilation Problems

von Tiberiu Constantinescu
Buchcover Schur Parameters, Factorization and Dilation Problems | Tiberiu Constantinescu | EAN 9783034899109 | ISBN 3-0348-9910-6 | ISBN 978-3-0348-9910-9

Schur Parameters, Factorization and Dilation Problems

von Tiberiu Constantinescu

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.