Orthogonal Rational Functions: 5 (Cambridge Monographs on Applied and Computational Mathematics, Series Number 5) - Softcover

Bultheel, Adhemar

Softcover

ISBN 10: 0521115914 ISBN 13: 9780521115919

Publisher: Cambridge University Press, 2009

Synopsis

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.

About this title

Review

'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

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. This theory has applications in theoretical real analysis, complex analysis, approximation theory, numerical analysis, and electrical engineering.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2009
• ISBN 10: 0521115914
• ISBN 13: 9780521115919
• Binding: Paperback
• Language: English
• Edition number: 1
• Number of pages: 424