- Volume
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2 ISBN 9783034804271
Description
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 Caratheodory functions and maximal weight solutions for particular matricial moment problems on the unit circle.
- Volume
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[1] ISBN 9783764375461
Description
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 Caratheodory functions and to the solutions of problems for these classes.
Table of Contents
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 Pseudocontinuable Schur Functions.- The Matricial Caratheodory Problem in Both Nondegenerate and Degenerate Cases.- A Gohberg-Heinig Type Inversion Formula Involving Hankel Operators.
by "Nielsen BookData"