Linear Operators and Linear Systems

Interpolation, Schur Functions and Moment Problems

Editors: Alpay, Daniel, Gohberg, Israel (Eds.)

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About this book

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.

Table of contents (7 chapters)

  • Basic Boundary Interpolation for Generalized Schur Functions and Factorization of Rational J-unitary Matrix Functions

    Alpay, Daniel (et al.)

    Pages 1-29

  • Discrete Analogs of Canonical Systems with Pseudo-exponential Potential. Inverse Problems

    Alpay, Daniel (et al.)

    Pages 31-65

  • Boundary Nevanlinna—Pick Interpolation Problems for Generalized Schur Functions

    Bolotnikov, Vladimir (et al.)

    Pages 67-119

  • A Truncated Matricial Moment Problem on a Finite Interval

    Choque Rivero, Abdon E. (et al.)

    Pages 121-173

  • Shift Operators Contained in Contractions, Schur Parameters and Pseudocontinuable Schur Functions

    Dubovoy, V. K.

    Pages 175-250

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-3-7643-7547-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-3-7643-7546-1
  • Free shipping for individuals worldwide
  • This title is currently reprinting. You can pre-order your copy now.
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Bibliographic Information

Bibliographic Information
Book Title
Interpolation, Schur Functions and Moment Problems
Editors
  • Daniel Alpay
  • Israel Gohberg
Series Title
Linear Operators and Linear Systems
Series Volume
165
Copyright
2006
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-7643-7547-8
DOI
10.1007/3-7643-7547-7
Hardcover ISBN
978-3-7643-7546-1
Edition Number
1
Number of Pages
XI, 304
Topics