Chebyshev Splines and Kolmogorov Inequalities

Inhaltsverzeichnis

• 0 Introduction.
• 1 Auxiliary Results.
• 2 Maximization of Functionals in H? [a, b] and Perfect ?-Splines.
• 3 Fredholm Kernels.
• 4 Review of Classical Chebyshev Polynomial Splines.
• 5 Additive Kolmogorov-Landau Inequalities.
• 6 Proof of the Main Result.
• 7 Properties of Chebyshev ?-Splines.
• 8 Chebyshev ?-Splines on the Half-line ?+.
• 9 Maximization of Integral Functional in H?[a1, a2], -? ? a1 < a2 ? +?.
• 10 Sharp Kolmogorov Inequalities in WrH?(?).
• 11 Landau and Hadamard Inequalities in WrH?(?+) and WrH?(?).
• 12 Sharp Kolmogorov-Landau inequalities in W2H?(?) AND W2H?(?+.
• 13 Chebyshev ?-Splines in the Problem of N-Width of the Functional Class WrH?[0, 1].
• 14 Function in WrH?[-1, 1] Deviating Most from Polynomials of Degree r.
• 15 N-Widths of the Class WrH?[-1, 1].
• 16 Lower Bounds for the N-Widths of the Class WrH?[n].
• Appendix A Kolmogorov Problem for Functions.
• A.3 Sufficient conditions of extremality in the problem (K - L).
• A.3.1 Corollaries of differentiation formulas.
• A.3.2 Extremality conditions in the form of an operator equation.
• A.4.2 Solution of the problem (K).
• A.4.3 Problem (K) in the Hölder classes.
• B.1 Preliminary remarks.
• B.2 Maximization of the norm.
• B.2.1 Differentiation formulae and inequalities.
• B.3 Maximization of the norm.
• B.4 Maximization of the norm.
• B.5 Maximization of the norm.