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Orthogonal Rational Functions: Cambridge Monographs on Applied and Computational Mathematics, cartea 5

Autor Adhemar Bultheel, Pablo Gonzalez-Vera, Erik Hendriksen, Olav Njastad
en Limba Engleză Paperback – 22 iul 2009
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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Specificații

ISBN-13: 9780521115919
ISBN-10: 0521115914
Pagini: 424
Ilustrații: 18 b/w illus.
Dimensiuni: 152 x 229 x 24 mm
Greutate: 0.62 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Cambridge Monographs on Applied and Computational Mathematics

Locul publicării:New York, United States

Cuprins

List of symbols; Introduction; 1. Preliminaries; 2. The fundamental spaces; 3. The kernel functions; 4. Recurrence and second kind functions; 5. Para-orthogonality and quadrature; 6. Interpolation; 7. Density of the rational functions; 8. Favard theorems; 9. Convergence; 10. Moment problems; 11. The boundary case; 12. Some applications; Conclusion; Bibliography; Index.

Recenzii

'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

Descriere

The book generalises the classical theory of orthogonal polynomials to rational functions.