000			02632nam a22003738i 4500
001			CR9780511530050
003			UkCbUP
005			20200124160228.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090409s1999||||enk o ||1 0|eng|d
020			_a9780511530050 (ebook)
020			_z9780521650069 (hardback)
020			_z9780521115919 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	4	_aQA404.5 _b.B85 1999
082	0	0	_a515/.55 _221
100	1		_aBultheel, Adhemar, _eauthor.
245	1	0	_aOrthogonal rational functions / _cAdhemar Bultheel [and others].
264		1	_aCambridge : _bCambridge University Press, _c1999.
300			_a1 online resource (xiv, 407 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge monographs on applied and computational mathematics ; _v5
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_a1. 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.
520			_aThis 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.
650		0	_aFunctions, Orthogonal.
650		0	_aFunctions of complex variables.
776	0	8	_iPrint version: _z9780521650069
830		0	_aCambridge monographs on applied and computational mathematics ; _v5.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511530050
999			_c517397 _d517395