Orthogonal Rational Functions (Hardcover)

Adhemar Bultheel

ISBN 10: 0521650062 / ISBN 13: 9780521650069

Editore: Cambridge University Press, Cambridge, 1999

Riguardo questo articolo

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 multiple locations in the US or from the UK, depending on stock availability.

Codice articolo 9780521650069

Dati bibliografici

• Titolo: Orthogonal Rational Functions (Hardcover)
• Editore: Cambridge University Press, Cambridge
• Data di pubblicazione: 1999
• Lingua: Inglese
• ISBN 10: 0521650062
• ISBN 13: 9780521650069
• Rilegatura: Hardcover
• Condizione: new

Descrizione articolo

Riassunto

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

Recensione

'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