Orthogonal Rational Functions A. Bultheel

ISBN: 9780521115919

Published: July 23rd 2009

Paperback

424 pages


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Orthogonal Rational Functions  by  A. Bultheel

Orthogonal Rational Functions by A. Bultheel
July 23rd 2009 | Paperback | PDF, EPUB, FB2, DjVu, audiobook, mp3, ZIP | 424 pages | ISBN: 9780521115919 | 7.13 Mb

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 whereMoreThis 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.



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