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Interpolation, Schur Functions and Moment Problems

  • Daniel Alpay
  • Israel Gohberg

Part of the Operator Theory: Advances and Applications book series (OT, volume 165)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Vladimir Bolotnikov, Alexander Kheifets
    Pages 67-119
  3. Abdon E. Choque Rivero, Yuriy M. Dyukarev, Bernd Fritzsche, Bernd Kirstein
    Pages 121-173
  4. Bernd Fritzsche, Bernd Kirstein, Andreas Lasarow
    Pages 251-290
  5. G. J. Groenewald, M. A. Kaashoek
    Pages 291-302
  6. Back Matter
    Pages 303-303

About this book

Introduction

Schur analysis originates with an 1917 article of Schur where he associated to a function, which is analytic and contractive in the open unit disk, a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients. In signal processing, they are often named reflection coefficients. Under the word "Schur analysis" one encounters a variety of problems related to Schur functions, such as interpolation problems, moment problems, the study of the relationships between the Schur coefficients and the properties of the function, or the study of underlying operators. Such questions are also considered for some generalizations of Schur functions. Furthermore, there is an extension of the notion of a Schur function for functions that are analytic and have a positive real part in the open upper half-plane; these functions are called Carathéodory functions.

This volume is almost entirely dedicated to the analysis of Schur and Carathéodory functions and to the solutions of problems for these classes.

Keywords

Factorization Interpolation Inverse problems Matrix Moment problem Shift operator

Editors and affiliations

  • Daniel Alpay
    • 1
  • Israel Gohberg
    • 2
  1. 1.Department of MathematicsBen-Gurion University of the NegevBeer ShevaIsrael
  2. 2.School of Mathematical Sciences, Raymond and Beverly Sackler, Faculty of Exact SciencesTel Aviv UniversityRamat AvivIsrael

Bibliographic information