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Orthogonal Rational Functions: 5 (Cambridge Monographs on Applied and Computational Mathematics, Series Number 5) - Hardcover
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.
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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.
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- PublisherCambridge University Press
- Publication date1999
- ISBN 10 0521650062
- ISBN 13 9780521650069
- BindingHardcover
- LanguageEnglish
- Number of pages424
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Orthogonal Rational Functions [Relié] Bultheel, Adhemar; Gonzalez-Vera, Pablo; Hendriksen, Erik et Njastad, Olav
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Orthogonal Rational Functions: 5 (Cambridge Monographs on Applied and Computational Mathematics, Series Number 5)
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Orthogonal Rational Functions: 5 (Cambridge Monographs on Applied and Computational Mathematics, Series Number 5)
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Orthogonal Rational Functions
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Orthogonal Rational Functions
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Hardcover. Condition: new. Hardcover. 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. 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. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. Seller Inventory # 9780521650069
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