Interpolation, Schur Functions and Moment Problems

✍ Scribed by Daniel Alpay, Israel Gohberg

• Publisher: Birkhäuser Basel
• Year: 2006
• Tongue: English
• Leaves: 309
• Series: Operator Theory: Advances and Applications 165
• Edition: 1
• Category: Library

✦ Synopsis

Schur analysis originates with a 1917 paper by Schur where he associated to a function 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 called reflection coefficients. Under the word "Schur analysis" one encounters a variety of problems related to Schur functions such as interpolation problems, moment problems, study of the relationships between the Schur coefficients and the properties of the function, study of underlying operators and others.

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

0front-matter......Page 1
1Basic Boundary Interpolation for Generalized Schur Functions and Factorization of Rational J-unitary Matrix Functions......Page 11
2Discrete Analogs of Canonical Systems with Pseudo-exponential Potential. Inverse Problems......Page 40
3Boundary Nevanlinna—Pick Interpolation Problems for Generalized Schur Functions......Page 75
4A Truncated Matricial Moment Problem on a Finite Interval......Page 128
5Shift Operators Contained in Contractions, Schur Parameters and Pseudocontinuable Schur Functions......Page 181
6The Matricial Carathéodory Problem in Both Nondegenerate and Degenerate Cases......Page 257
7A Gohberg-Heinig Type Inversion Formula Involving Hankel Operators......Page 297
back-matter......Page 309