Interpolation, Schur Functions and Moment Problems
Schur analysis originated with an 1917 article which 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, often named reflection coefficients in signal processing. This volume comprises seven essays dedicated to the analysis of Schur and Carathéodory functions and to the solutions of problems for these classes.
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Book Description
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.
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Table of Contents
Editorial introduction.- Basic Boundary Interpolation for Generalized Schur Functions and Factorization of Rational J-Unitary Matrix Functions.- Discrete Analogs of Canonical Systems with Pseudo-exponential Potential. Inverse Problems.- Boundary Nevanlinna-Pick Interpolation Problems for Generalized Schur Functions.- A Truncated Matricial Moment Problem on a Finite Interval.- Shift Operators Contained in Contractions, Schur Parameters and Pseudo-continuable Schur Functions.- The Matricial Carathéodory Problem in Both Nondegenerate and Degenerate Cases.- A Gohberg-Heinig Type Inversion Formula Involving Hankel Operators.
