Algebraic Approximation: A Guide To Past And Current Solutions by Jorge BustamanteAlgebraic Approximation: A Guide To Past And Current Solutions by Jorge Bustamante

Algebraic Approximation: A Guide To Past And Current Solutions

byJorge Bustamante

Paperback | November 16, 2011

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This book contains an exposition of several results related with direct and converse theorems in the theory of approximation by algebraic polynomials in a finite interval. In addition, some facts concerning trigonometric approximation that are necessary for motivation and comparisons are included. The selection of papers that are referenced and discussed document some trends in polynomial approximation from the 1950s to the present day.
Title:Algebraic Approximation: A Guide To Past And Current SolutionsFormat:PaperbackDimensions:205 pagesPublished:November 16, 2011Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3034801939

ISBN - 13:9783034801935

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Table of Contents

Preface.- 1 Some Notes on Trigonometric Approximation.- Early years.- Direct and converse results: a motivation.- Some asymptotic results.- 2 The End Points Effect.- Two different problems.- Nikolskii's discovery.- Problems connected with Nikolskii's result.- Timan-type estimates.- Estimates with higher-order moduli.- Gopengauz-Teliakovskii-type estimates.- Characterization of some classes of functions.- Simultaneous approximation.- Zamansky-type estimates.- Fuksman-Potapov solution to the second problem.- Integral metrics.- Lp, 0 <_20_1.-20_thewhitney20_theorem.-20_other20_classes20_of20_functions.-20_320_looking20_for20_new20_moduli.-20_the20_works20_of20_potapov.-20_butzer20_and20_the20_method20_of20_fourier20_transforms.-20_the20_3f_20_modulus20_of20_ivanov.-20_ditzian-totik20_moduli.-20_felten20_modulus.-20_420_exact20_estimates20_and20_asymptotics.-20_asymptotics20_for20_lip128_m2c_5b_3f_12c_15d_.-20_estimates20_for20_wr.-20_asymptotics20_for20_cr2c_w5b_3f_12c_15d_.-20_estimates20_for20_integrable20_functions.-20_pointwise20_asymptotics.-20_520_construction20_of20_special20_operators.-20_estimates20_in20_norm.-20_timan-type20_estimates.-20_gopengauz20_estimates.-20_bernstein20_interpolation20_process.-20_integral20_operators.-20_simultaneous20_approximation.-20_estimation20_with20_constants.-20_the20_boolean20_sums20_approach.-20_discrete20_operators.-20_bibliography.-20_index. 1.-="" thewhitney="" theorem.-="" other="" classes="" of="" functions.-="" 3="" looking="" for="" new="" moduli.-="" the="" works="" potapov.-="" butzer="" and="" method="" fourier="" transforms.-="" modulus="" ivanov.-="" ditzian-totik="" felten="" modulus.-="" 4="" exact="" estimates="" asymptotics.-="" asymptotics="" _lip128_m2c_5b_3f_12c_15d_.-="" wr.-="" _cr2c_w5b_3f_12c_15d_.-="" integrable="" pointwise="" 5="" construction="" special="" operators.-="" in="" norm.-="" timan-type="" estimates.-="" gopengauz="" bernstein="" interpolation="" process.-="" integral="" simultaneous="" approximation.-="" estimation="" with="" constants.-="" boolean="" sums="" approach.-="" discrete="" bibliography.-="">

Editorial Reviews

From the reviews:"The monograph presents an exposition of results related to direct and converse theorems in the theory of approximation by algebraic polynomials in a finite interval. . The main achievement of the book is that it gathers some different known solutions to problems in algebraic approximation that are not collected in other text books. . this book is a very helpful tool for students and researchers interested in approximation by algebraic polynomials." (Daniel Cárdenas-Morales, Zentralblatt MATH, Vol. 1248, 2012)