Orthogonal Rational Functions (Cambridge Monographs on Applied and Computational Mathematics)
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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 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.
Orthogonal Rational Functions (Cambridge Monographs on Applied and Computational Mathematics),A. Bultheel,P. Gonzalez-Vera,E. Hendriksen,O. Njastad,M. J. Ablowitz,S. H. Davis,E. J. Hinch,A. Iserles,J. Ockendon,P. J. Olver,Cambridge University Press,0521650062,Applied,Calculus,Differential Equations,Engineering - Electrical & Electronic,Fourier Analysis,Functions Of Complex Variables,Functions, Orthogonal,Mathematical Analysis,Mathematics,Science/Mathematics,Applied mathematics,Calculus & mathematical analysis,Mathematics / Mathematical Analysis
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