Linear Operators and Linear Systems

Interpolation, Schur Functions and Moment Problems II

Editors: Alpay, Daniel, Kirstein, Bernd (Eds.)

  • Focus on new results and original research
  • Most approaches and techniques presented for the first time in an easily understandable format
  • Topics covered reflect new trends in Schur analysis and new areas for future studies
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About this book

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.​

Reviews

From the reviews:

“The contributors of this volume are very productive and they have published a large number of papers in many journals and books. … It may take a while for the reader to get used to it, but once familiar with these habits and the constructs involved, it is good reading. It will be of high interest to anyone who is involved from far or near with Schur analysis and the whole universe of related topics that I sketched in the beginning.” (A. Bultheel, The European Mathematical Society, September, 2012)


Table of contents (6 chapters)

  • On the Concept of Invertibility for Sequences of Complex $$ p \times q $$ -matrices and its Application to Holomorphic $$ p \times q $$ -matrix-valued Functions

    Fritzsche, Bernd (et al.)

    Pages 9-56

  • On Reciprocal Sequences of Matricial Carathéodory Sequences and Associated Matrix Functions

    Fritzsche, Bernd (et al.)

    Pages 57-115

  • On a Schur-type Algorithm for Sequences of Complex $${p} \times{q} $$ -matrices and its Interrelations with the Canonical Hankel Parametrization

    Fritzsche, Bernd (et al.)

    Pages 117-192

  • Multiplicative Structure of the Resolvent Matrix for the Truncated Hausdorff Matrix Moment Problem

    Rivero, Abdon Eddy Choque

    Pages 193-210

  • On a Special Parametrization of Matricial α-Stieltjes One-sided Non-negative Definite Sequences

    Fritzsche, Bernd (et al.)

    Pages 211-250

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-0348-0428-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-3-0348-0427-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-3-0348-0742-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Interpolation, Schur Functions and Moment Problems II
Editors
  • Daniel Alpay
  • Bernd Kirstein
Series Title
Linear Operators and Linear Systems
Series Volume
226
Copyright
2012
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0428-8
DOI
10.1007/978-3-0348-0428-8
Hardcover ISBN
978-3-0348-0427-1
Softcover ISBN
978-3-0348-0742-5
Edition Number
1
Number of Pages
VI, 302
Topics