Orthogonal Rational Functions

A. Bultheel

ISBN 10: 0521650062 / ISBN 13: 9780521650069

Published by Cambridge University Press, 1999

About this Item

Druck auf Anfrage Neuware - Printed after ordering - This book generalises the classical theory of orthogonal polynomials on the complex unit circle, or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. The first part treats the case where these poles are all outside the unit disk or in the lower half plane. Classical topics such as recurrence relations, numerical quadrature, interpolation properties, Favard theorems, convergence, asymptotics, and moment problems are generalised and treated in detail. The same topics are discussed for the different situation where the poles are located on the unit circle or on the extended real line. In the last chapter, several applications are mentioned including linear prediction, Pisarenko modelling, lossless inverse scattering, and network synthesis. This theory has many applications in theoretical real and complex analysis, approximation theory, numerical analysis, system theory, and in electrical engineering.

Seller Inventory # 9780521650069

Bibliographic Details

• Title: Orthogonal Rational Functions
• Publisher: Cambridge University Press
• Publication Date: 1999
• Language: English
• ISBN 10: 0521650062
• ISBN 13: 9780521650069
• Binding: Buch
• Condition: Neu
• Dimensions: 235W x 157H x 29D millimeters 235 millimeters width by 157 millimeters height by 29 millimeters depth
• Weight: 836 grams

About this title

Synopsis

This volume generalizes the classical theory of orthogonal polynomials on the complex unit circle or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. The first part treats the case where these poles are all outside the unit disk or in the lower half plane. Classical topics such as recurrence relations, numerical quadrature, interpolation properties, Favard theorems, convergence, asymptotics, and moment problems are generalized and treated in detail. The same topics are discussed for a different situation where the poles are located on the unit circle or on the extended real line. In the last chapter, several applications are mentioned including linear prediction, Pisarenko modeling, lossless inverse scattering, and network synthesis. This theory has many applications both in theoretical real and complex analysis, approximation theory, numerical analysis, system theory, and electrical engineering.

Book Description

This book generalizes the classical theory of orthogonal polynomials on the complex unit circle or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. This theory has many applications both in theoretical real and complex analysis, approximation theory, numerical analysis, system theory, and in electrical engineering.