Chebyshev Splines and Kolmogorov Inequalities
Springer Basel (Verlag)
978-3-0348-9781-5 (ISBN)
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.
Erscheint lt. Verlag | 3.10.2013 |
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Reihe/Serie | Operator Theory: Advances and Applications |
Zusatzinfo | XIII, 210 p. |
Verlagsort | Basel |
Sprache | englisch |
Maße | 170 x 244 mm |
Gewicht | 400 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
Schlagworte | Analysis • Calculus • Equation • Function • Optimization • Theorem • Topology |
ISBN-10 | 3-0348-9781-2 / 3034897812 |
ISBN-13 | 978-3-0348-9781-5 / 9783034897815 |
Zustand | Neuware |
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