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Orthogonal Rational Functions Adhemar Bultheel (Katholieke Universiteit Leuven, Belgium)

Orthogonal Rational Functions By Adhemar Bultheel (Katholieke Universiteit Leuven, Belgium)

Summary

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.

Orthogonal Rational Functions Summary

Orthogonal Rational Functions by Adhemar Bultheel (Katholieke Universiteit Leuven, Belgium)

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.

Orthogonal Rational Functions 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

Table of Contents

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.

Additional information

NPB9780521650069
9780521650069
0521650062
Orthogonal Rational Functions by Adhemar Bultheel (Katholieke Universiteit Leuven, Belgium)
New
Hardback
Cambridge University Press
1999-02-13
424
N/A
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