000			05493nam a2200349 i 4500
001			8994
005			20250417120606.0
008			930208s1993 gw b 001 0 eng
010			_a93018420
020			_a3540506276
020			_a0387506276
040			_aDLC _erda _cDLC _dCWR
041	0		_aeng
049			_aBAUN_MERKEZ
050	0	4	_aQA221 _b.D44 1993
082	0	0	_220
100	1		_aDeVore, Ronald A _985734 _eaut
245	1	0	_aConstructive approximation / _cRonald A. DeVore, George G. Lorentz
264		1	_aBerlin ; _aNew York : _bSpringer-Verlag, _c[1993]
264		4	_c©1993
300			_ax, 449 pages : _billustrations ; _c24 cm
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
490	1		_aGrundlehren der mathematischen Wissenschaften ; _v303
504			_aIncludes bibliographical references (pages [434]-446) and index
505	0	0	_tContents _tCh. 1 Theorems of Weierstrass _t1 Basic Notions _t2 Approximation by Integral Operators _t3 The Theorem of Korovkin _t4 Theorems of Stone-Weierstrass _tCh. 2 Spaces of Functions _t1 Introduction. The Spaces C and L[subscript p] _t2 Rearrangement-Invariant Function Spaces _t3 Hardy's Inequalities and the ([theta],q)-quasi-norms _t4 Linear Operators. Interpolation of Operators _t5 Spaces of Differentiable Functions: Sobolev Spaces _t6 Moduli of Continuity _t7 Moduli of Smoothness _t8 Marchaud Inequalities _t9 Lipschitz Spaces _t10 Besov Spaces _tCh. 3 Best Approximation _t1 Introduction: Existence of Best Approximation _t2 Kolmogorov's Theorem _t3 Haar Systems _t4 Uniqueness of Best Approximation in C(A) _t5 Chebyshev's Theorem _t6 Chebyshev Polynomials _t7 Strong Unicity _t8 Remez Algorithms _t9 Krein's Theorem _t10 Best Approximation in L[subscript p], [actual symbol not reproducible] _t11 Polya and Descartes Systems _t12 Weak Haar Systems _tCh. 4 Properties of Polynomials _t1 Inequalities of Bernstein, Szego and Markov _t2 Polynomials on the Complex Plane and in Banach Spaces _t3 Bernstein Inequalities in L[subscript p], 0 < p < 1 _t4 Polynomials with Positive Coefficients in x, 1 - x _t5 Lagrange Interpolation _t6 Hermite Interpolation _t7 Divided Differences _t8 Quadrature Formulas _t9 Birkhoff Interpolation _t10 Regularity of Birkhoff Matrices _tCh. 5 Splines _t1 Definitions and Simple Properties _t2 B-Splines _t3 B-Spline Series _t4 Quasi-Interpolant Operators _t5 Euler and Bernoulli Splines _t6 Definition of Splines by Their Extremal Properties _t7 The Kolmogorov-Landau Inequalities _t8 Zero Count for Splines _t9 Spline Interpolation _t10 Sign Variation of Splines _t11 Total Positivity of the B-Spline Collocation Matrix _tCh. 6 K-Functionals and Interpolation Spaces _t1 K-Functionals _t2 K-Functionals and Moduli of Smoothness _t3 Comparisons of Moduli of Smoothness _t4 Two Theorems of Whitney _t5 Averaged Moduli of Smoothness _t6 Moduli of Smoothness with Weights _t7 The [theta],q-Interpolation Spaces _tCh. 7 Central Theorems of Approximation _t2 Trigonometric Approximation _t3 Inverse Theorems of Trigonometric Approximation _t4 Favard's Theorems _t5 Improvement of Estimates _t6 Approximation by Algebraic Polynomials _t7 Spline Approximation _t8 Approximation of Analytic Functions _t9 Approximation Spaces _tCh. 8 Influence of Endpoints in Polynomial Approximation _t2 Local Inequalities for Polynomials _t3 Properties of the Jackson Operators P[subscript n,m](f) _t4 Simultaneous Approximation of Functions and Their Derivatives _t5 Brudnyi's Theorem _t6 Inverse Theorems _t7 Approximation Spaces for Algebraic Polynomials _tCh. 9 Approximation by Operators _t2 Computation of Some Norms _t3 Examples of Linear Polynomial Operators _t4 Positive Operators _t5 Projections onto Spaces Spanned by Exponentials _t6 Lower Bounds _t7 Projections in Arbitrary Banach Spaces _t8 Families of Commuting Operators _tCh. 10 Bernstein Polynomials _t1 Definitions and Inequalities _t2 Derivatives of Bernstein Polynomials _t3 Approximation and Shape Preserving Properties _t4 Bernstein Polynomials of Convex Functions _t5 Saturation and Inverse Theorems _t6 Saturation Theorems for Kantorovich Polynomials _t7 Characterization of Approximation Spaces _t8 Further Properties and Variants of Bernstein Polynomials Weak Haar Spaces _tCh. 11 Approximation of Classes of Functions, Muntz Theorems _t1 Approximation by Fourier Sums _t2 Saturation Classes _t3 Saturation of the Fejer Operators _t4 Theorems of Korneichuk _t5 Muntz' Theorem. Approximation of Monomials _t6 Case When [actual symbol not reproducible]. Selection of Best Powers _tCh. 12 Spline Approximation _t2 Splines with Equally Spaced Knots _t3 Approximation by Dyadic Splines _t4 Splines with Free Knots _t5 Smoothness in L[subscript p] for 0 < p < 1 _t6 Dyadic Splines in L[subscript p], 0 < p < 1 _t7 Comparison of the Spaces [actual symbol not reproducible] _t8 Free Knot Spline Approximation in L[subscript p], 0 < p < [actual symbol not reproducible] _tCh. 13 Spline Interpolation and Projections onto Spline Spaces _t1 Introduction. Lagrange Interpolation by Splines _t2 Selection of Interpolation Points _t3 Cubic Spline Interpolation _t4 Orthogonal Projection onto Splines _t5 Interpolation on R _t6 Cardinal Spline Interpolation _t7 Approximation from Shift Invariant Spaces _t8 Shape Preserving Interpolation _t9 Shape Preserving Quadratic Spline Interpolation _tBibliography _tIndex
650		0	_aApproximation theory _9118740
700	1		_aLorentz, G. G _989467 _eaut
830		0	_978749 _aGrundlehren der mathematischen Wissenschaften ; _v303
942			_2lcc _cKT
999			_c6911 _d6911