Chebyshev Splines and Kolmogorov Inequalities by Sergey BagdasarovChebyshev Splines and Kolmogorov Inequalities by Sergey Bagdasarov

Chebyshev Splines and Kolmogorov Inequalities

bySergey Bagdasarov

Paperback | October 3, 2013

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Since the introduction of the functional classes HW (lI) and WT HW (lI) and their peri­ odic analogs Hw (1I') and <_.20_therefore2c_20_no20_advance20_in20_the20_t20_exact20_and20_complete20_solution20_of20_problems20_in20_the20_nonperiodic20_classes20_w20_hw20_could20_be20_expected20_without20_finding20_analogs20_of20_polynomial20_perfect20_splines20_in20_wt20_hw20_. _therefore2c_="" no="" advance="" in="" the="" t="" exact="" and="" complete="" solution="" of="" problems="" nonperiodic="" classes="" w="" hw="" could="" be="" expected="" without="" finding="" analogs="" polynomial="" perfect="" splines="" wt="">
Title:Chebyshev Splines and Kolmogorov InequalitiesFormat:PaperbackDimensions:210 pages, 24.4 × 17 × 0.01 inPublished:October 3, 2013Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3034897812

ISBN - 13:9783034897815

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Table of Contents

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 <_20_a220_3f_20_2b_3f_.-20_1020_sharp20_kolmogorov20_inequalities20_in20_wrh3f_28_3f_29_.-20_1120_landau20_and20_hadamard20_inequalities20_in20_wrh3f_28_3f_2b_29_20_and20_wrh3f_28_3f_29_.-20_1220_sharp20_kolmogorov-landau20_inequalities20_in20_w2h3f_28_3f_29_20_and20_w2h3f_28_3f_2b_.-20_1320_chebyshev20_3f_-splines20_in20_the20_problem20_of20_n-width20_of20_the20_functional20_class20_wrh3f_5b_02c_20_15d_.-20_1420_function20_in20_wrh3f_5b_-12c_20_15d_20_deviating20_most20_from20_polynomials20_of20_degree20_r.-20_1520_n-widths20_of20_the20_class20_wrh3f_5b_-12c_20_15d_.-20_1620_lower20_bounds20_for20_the20_n-widths20_of20_the20_class20_wrh3f_5b_n5d_.-20_appendix20_a20_kolmogorov20_problem20_for20_functions.-20_a.320_sufficient20_conditions20_of20_extremality20_in20_the20_problem20_28_k20_-20_l29_.-20_a.3.120_corollaries20_of20_differentiation20_formulas.-20_a.3.220_extremality20_conditions20_in20_the20_form20_of20_an20_operator20_equation.-20_a.4.220_solution20_of20_the20_problem20_28_k29_.-20_a.4.320_problem20_28_k29_20_in20_the20_hc3b6_lder20_classes.-20_b.120_preliminary20_remarks.-20_b.220_maximization20_of20_the20_norm.-20_b.2.120_differentiation20_formulae20_and20_inequalities.-20_b.320_maximization20_of20_the20_norm.-20_b.420_maximization20_of20_the20_norm.-20_b.520_maximization20_of20_the20_norm. a2="" _2b_3f_.-="" 10="" sharp="" kolmogorov="" inequalities="" in="" _wrh3f_28_3f_29_.-="" 11="" landau="" and="" hadamard="" _wrh3f_28_3f_2b_29_="" 12="" kolmogorov-landau="" _w2h3f_28_3f_29_="" _w2h3f_28_3f_2b_.-="" 13="" chebyshev="" splines="" the="" problem="" of="" n-width="" functional="" class="" _wrh3f_5b_02c_="" _15d_.-="" 14="" function="" _wrh3f_5b_-12c_="" _15d_="" deviating="" most="" from="" polynomials="" degree="" r.-="" 15="" n-widths="" 16="" lower="" bounds="" for="" _wrh3f_5b_n5d_.-="" appendix="" a="" functions.-="" a.3="" sufficient="" conditions="" extremality="" _28_k="" -="" _l29_.-="" a.3.1="" corollaries="" differentiation="" formulas.-="" a.3.2="" form="" an="" operator="" equation.-="" a.4.2="" solution="" _28_k29_.-="" a.4.3="" _28_k29_="" _hc3b6_lder="" classes.-="" b.1="" preliminary="" remarks.-="" b.2="" maximization="" norm.-="" b.2.1="" formulae="" inequalities.-="" b.3="" b.4="" b.5="">