Orthogonal Rational Functions

Adhemar Bultheel (Katholieke Universiteit Leuven, Belgium),Pablo Gonzalez-Vera (Universidad de la Laguna, Tenerife),Erik Hendriksen (Universiteit van Amsterdam),Olav Njastad (Norges Teknisk-Naturvitenskapelige Universitet (Ntnu), Norway)

Orthogonal Rational Functions
Format
Paperback
Publisher
Cambridge University Press
Country
United Kingdom
Published
23 July 2009
Pages
424
ISBN
9780521115919

Orthogonal Rational Functions

Adhemar Bultheel (Katholieke Universiteit Leuven, Belgium),Pablo Gonzalez-Vera (Universidad de la Laguna, Tenerife),Erik Hendriksen (Universiteit van Amsterdam),Olav Njastad (Norges Teknisk-Naturvitenskapelige Universitet (Ntnu), Norway)

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.

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