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  1. Home
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  3. Orthogonal Rational Functions
  • Cited by 93
Publisher:
Cambridge University Press
Online publication date:
October 2009
Print publication year:
1999
Online ISBN:
9780511530050
DOI:
https://doi.org/10.1017/CBO9780511530050
Subjects:
Mathematics, Computational Science, Numerical Analysis and Computational Science
Series:
Cambridge Monographs on Applied and Computational Mathematics (5)
Information

Book description

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.

Reviews

‘The text is written with great clarity … A book with four authors is not common, but these four … are to be applauded for their achievement.’

J. H. McCabe

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