Interpolation, Schur functions and moment problems II [electronic resource] /
Alpay, Daniellateditor.
Kirstein, Bernd.editor.
The origins of Schur analysis lie in a 1917 article by Issai Schur in which he constructed a numerical sequence to correspond to a holomorphic contractive function on the unit disk. These sequences are now known as Schur parameter sequences. Schur analysis has grown significantly since its beginnings in the early twentieth century and now encompasses a wide variety of problems related to several classes of holomorphic functions and their matricial generalizations. These problems include interpolation and moment problems as well as Schur parametrization of particular classes of contractive or nonnegative Hermitian block matrices. This book is primarily devoted to topics related to matrix versions of classical interpolation and moment problems. The major themes include Schur analysis of nonnegative Hermitian block Hankel matrices and the construction of Schur-type algorithms. This book also covers a number of recent developments in orthogonal rational matrix functions, matrix-valued Carathéodory functions and maximal weight solutions for particular matricial moment problems on the unit circle.
Description based upon print version of record.
8. Moore-Penrose pseudoinverses of holomorphic matrix-malued functionsAppendix A. The Moore-Penrose inverse of a complex matrix; References; On Reciprocal Sequences of Matricial Carathéodory Sequences and Associated Matrix Functions; 0. Introduction; 1. Reciprocal sequences; 2. Matricial Toeplitz non-negative definite sequences; 3. Matricial Carathéodory sequences; 4. Reciprocal sequences of matricial Carathéodory sequences; 5. Matricial Toeplitz non-negative definite sequences generated by reciprocation; 6. Matricial Carathéodory functions
Appendix B. On two particular multiplicative groups of triangular block matricesReferences; Multiplicative Structure of the Resolvent Matrix for the Truncated Hausdorff Matrix Moment Problem; 1. Introduction; 2. Notation and preliminaries; 2.1. Hausdorff matrix moment problem and the resolvent matrix; 2.2. The resolvent matrix of the HMM problem; 3. Main algebraic identities; 4. The Blaschke-Potapov factors; Appendix A. Blaschke-Potapov representation of the resolvent matrix, the case of an even number of moments; Acknowledgment; References
On a Special Parametrization of Matricial α-Stieltjes One-sided Non-negative Definite Sequences
Includes bibliographical references.
The origins of Schur analysis lie in a 1917 article by Issai Schur in which he constructed a numerical sequence to correspond to a holomorphic contractive function on the unit disk. These sequences are now known as Schur parameter sequences. Schur analysis has grown significantly since its beginnings in the early twentieth century and now encompasses a wide variety of problems related to several classes of holomorphic functions and their matricial generalizations. These problems include interpolation and moment problems as well as Schur parametrization of particular classes of contractive or nonnegative Hermitian block matrices. This book is primarily devoted to topics related to matrix versions of classical interpolation and moment problems. The major themes include Schur analysis of nonnegative Hermitian block Hankel matrices and the construction of Schur-type algorithms. This book also covers a number of recent developments in orthogonal rational matrix functions, matrix-valued Carathéodory functions and maximal weight solutions for particular matricial moment problems on the unit circle.
Operator theory.
Integral transforms.
Operational calculus.
Functions of complex variables.
Operator Theory.
Integral Transforms, Operational Calculus.
Functions of a Complex Variable.
Operator theory