- Description
- electronic text (305 p.) : digital
- Additional Authors
- Alpay, DanielKirstein, Bernd,
- Corporate Author
- SpringerLink (Online service)
- Notes
- "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."--Publisher's websiteIncludes bibliographical referencesOn the Concept of Invertibility for Sequences of Complex p x qpq -matrices and its Application to Holomorphic p x qpq -matrix-valued Functions / Bernd Fritzsche, Bernd Kirstein, Conrad Mädler and Tilo Schwarz -- On Reciprocal Sequences of Matricial Carathéodory Sequences and Associated Matrix Functions / Bernd Fritzsche, Bernd Kirstein, Andreas Lasarow and Armin Rahn -- On a Schur-type Algorithm for Sequences of Complex p x qpq -matrices and its Interrelations with the Canonical Hankel Parametrization / Bernd Fritzsche, Bernd Kirstein, Conrad Mädler and Tilo Schwarz -- Multiplicative Structure of the Resolvent Matrix for the Truncated Hausdorff Matrix Moment Problem / Abdon Eddy Choque Rivero -- On a Special Parametrization of Matricial [alpha]-Stieltjes One-sided Non-negative Definite Sequences / Bernd Fritzsche, Bernd Kirstein and Conrad Mädler -- On Maximal Weight Solutions of a Moment Problem for Rational Matrix-valued Functions / Bernd Fritzsche, Bernd Kirstein and Andreas Lasarow