Interpolation, Schur Functions and Moment Problems II

  • Daniel Alpay
  • Bernd Kirstein

Part of the Operator Theory: Advances and Applications book series (OT, volume 226)

Also part of the Linear Operators and Linear Systems book sub series (LOLS, volume 226)

Table of contents

About this book

Introduction

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.​

Keywords

Carathéodory and Nevanlinna classes Schur analysis Schur-type algorithms matrix versions of power moment problems

Editors and affiliations

  • Daniel Alpay
    • 1
  • Bernd Kirstein
    • 2
  1. 1.Dept. Mathematics & Computer ScienceBen-Gurion University of the NegevBeer ShevaIsrael
  2. 2., Mathematisches InstitutUniversität LeipzigLeipzigGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0428-8
  • Copyright Information Springer Basel 2012
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0427-1
  • Online ISBN 978-3-0348-0428-8
  • About this book