Ebook: Schur Parameters, Factorization and Dilation Problems

This book is devoted to the ubiquity of the Schur parameters. A dilation theoretic view leads to a unified perspective on several topics where Schur parameters appear as basic cells. Together with the transmission line, their physical counter- part, they appear in scattering theory, in modeling, prediction and filtering of nonstationary processes, in signal processing, geophysics and system theory. Modeling problems are considered for certain classes of operators, interpolation problems, determinental formulae, as well as connections with certain classes of graphs where, again, the Schur parameters could play a role. Some general algorithms that explore the transmission line are also presented in this book. As a whole, the text is self-contained and it is addressed to people interested in the previously mentioned topics or connections between them.

---

This book is devoted to the ubiquity of the Schur parameters. A dilation theoretic view leads to a unified perspective on several topics where Schur parameters appear as basic cells. Together with the transmission line, their physical counter- part, they appear in scattering theory, in modeling, prediction and filtering of nonstationary processes, in signal processing, geophysics and system theory. Modeling problems are considered for certain classes of operators, interpolation problems, determinental formulae, as well as connections with certain classes of graphs where, again, the Schur parameters could play a role. Some general algorithms that explore the transmission line are also presented in this book. As a whole, the text is self-contained and it is addressed to people interested in the previously mentioned topics or connections between them.
Content:
Front Matter....Pages i-ix
Schur Parameters and Positive Block Matrices....Pages 1-34
Models for Triangular Contractions....Pages 35-56
Moment Problems and Interpolation....Pages 57-91
Displacement Structures....Pages 93-126
Factorization of Positive Definite Kernels....Pages 127-153
Nonstationary Processes....Pages 155-177
Graphs and Completion Problems....Pages 179-202
Determinantal Formulae and Optimization....Pages 203-222
Back Matter....Pages 223-254

---

This book is devoted to the ubiquity of the Schur parameters. A dilation theoretic view leads to a unified perspective on several topics where Schur parameters appear as basic cells. Together with the transmission line, their physical counter- part, they appear in scattering theory, in modeling, prediction and filtering of nonstationary processes, in signal processing, geophysics and system theory. Modeling problems are considered for certain classes of operators, interpolation problems, determinental formulae, as well as connections with certain classes of graphs where, again, the Schur parameters could play a role. Some general algorithms that explore the transmission line are also presented in this book. As a whole, the text is self-contained and it is addressed to people interested in the previously mentioned topics or connections between them.
Content:
Front Matter....Pages i-ix
Schur Parameters and Positive Block Matrices....Pages 1-34
Models for Triangular Contractions....Pages 35-56
Moment Problems and Interpolation....Pages 57-91
Displacement Structures....Pages 93-126
Factorization of Positive Definite Kernels....Pages 127-153
Nonstationary Processes....Pages 155-177
Graphs and Completion Problems....Pages 179-202
Determinantal Formulae and Optimization....Pages 203-222
Back Matter....Pages 223-254
....