Interpolation, Schur Functions and Moment Problems II

✍ Scribed by Bernd Fritzsche, Bernd Kirstein (auth.), Daniel Alpay, Bernd Kirstein (eds.)

• Publisher: Birkhäuser Basel
• Year: 2012
• Tongue: English
• Leaves: 306
• Series: Operator Theory: Advances and Applications 226
• Edition: 1
• Category: Library

✦ Synopsis

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.​

✦ Table of Contents

Front Matter....Pages i-v
On the Concept of Invertibility for Sequences of Complex $$ p \times q $$ -matrices and its Application to Holomorphic $$ p \times q $$ -matrix-valued Functions....Pages 9-56
On Reciprocal Sequences of Matricial Carathéodory Sequences and Associated Matrix Functions....Pages 57-115
On a Schur-type Algorithm for Sequences of Complex $${p} \times{q} $$ -matrices and its Interrelations with the Canonical Hankel Parametrization....Pages 117-192
Multiplicative Structure of the Resolvent Matrix for the Truncated Hausdorff Matrix Moment Problem....Pages 193-210
On a Special Parametrization of Matricial α-Stieltjes One-sided Non-negative Definite Sequences....Pages 211-250
On Maximal Weight Solutions of a Moment Problem for Rational Matrix-valued Functions....Pages 251-300

✦ Subjects

Operator Theory; Integral Transforms, Operational Calculus; Functions of a Complex Variable