000			03798nam a22005175i 4500
001			978-3-540-68349-0
003			DE-He213
005			20161121231213.0
007			cr nn 008mamaa
008			100301s2008 gw | s |||| 0|eng d
020			_a9783540683490 _9978-3-540-68349-0
024	7		_a10.1007/978-3-540-68349-0 _2doi
050		4	_aQA431
072		7	_aPBKL _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515.45 _223
100	1		_aMastroianni, Giuseppe. _eauthor.
245	1	0	_aInterpolation Processes _h[electronic resource] : _bBasic Theory and Applications / _cby Giuseppe Mastroianni, Gradimir V. Milovanović.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2008.
300			_aXIV, 446 p. 42 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSpringer Monographs in Mathematics, _x1439-7382
505	0		_a1. Constructive Elements and Approaches in Approximation Theory -- 1.1 Introduction to Approximation Theory -- 1.2 Basic Facts on Trigonometric Approximation -- 1.3 Chebyshev Systems and Interpolation -- 1.4 Interpolation by Algebraic Polynomials -- 2. Orthogonal Polynomials and Weighted Polynomial Approximation -- 2.1 Orthogonal Systems and Polynomials -- 2.2 Orthogonal Polynomials on the Real Line -- 2.3 Classical Orthogonal Polynomials -- 2.4 Nonclassical Orthogonal Polynomials -- 2.5 Weighted Polynomial Approximation -- 3. Trigonometric Approximation -- 3.1 Approximating Properties of Operators -- 3.2 Discrete Operators -- 4. Algebraic Interpolation in Uniform Norm -- 4.1 Introduction and Preliminaries -- 4.2 Optimal Systems of Nodes -- 4.3 Weighted Interpolation -- 5. Applications -- 5.1 Quadrature Formulae -- 5.2 Integral Equations -- 5.3 Moment-Preserving Approximation -- 5.4 Summation of Slowly Convergent Series -- References -- Index.
520			_aThe classical books on interpolation address numerous negative results, i.e., results on divergent interpolation processes, usually constructed over some equidistant systems of nodes. The authors present, with complete proofs, recent results on convergent interpolation processes, for trigonometric and algebraic polynomials of one real variable, not yet published in other textbooks and monographs on approximation theory and numerical mathematics. In this special, but fundamental and important field of real analysis the authors present the state of art. Some 500 references are cited, including many new results of the authors. Basic tools in this field (orthogonal polynomials, moduli of smoothness, K-functionals, etc.) as well as some selected applications in numerical integration, integral equations, moment-preserving approximation and summation of slowly convergent series are also given. Beside the basic properties of the classical orthogonal polynomials the book provides new results on nonclassical orthogonal polynomials including methods for their numerical construction.
650		0	_aMathematics.
650		0	_aFourier analysis.
650		0	_aIntegral equations.
650		0	_aSequences (Mathematics).
650		0	_aSpecial functions.
650	1	4	_aMathematics.
650	2	4	_aIntegral Equations.
650	2	4	_aSpecial Functions.
650	2	4	_aSequences, Series, Summability.
650	2	4	_aFourier Analysis.
700	1		_aMilovanović, Gradimir V. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783540683469
830		0	_aSpringer Monographs in Mathematics, _x1439-7382
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-540-68349-0
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c510076 _d510076