History of Approximation Theory (eBook)

Dedication Foreword Preface Introduction Forerunners 1.1 Euler’s Analysis of Delisle’s Map 1.2 Laplace’s Approximation of Earth’s Surface Pafnuti Lvovich Chebyshev 2.1 Chebyshev’s Curriculum Vitae 2.2 Stimuli for the Development of a Theory 2.3 First Theoretical Approaches 2.4 First Theoretical Compositions 2.5 Theory of Orthogonal Polynomials 2.6 Other Contributions of P. L. Chebyshev 2.7 Chebyshev - Euler of the 18th Century? The Saint Petersburg Mathematical School 3.1 Aleksandr Nikolaevich Korkin 3.2 Egor Ivanovich Zolotarev 3.3 Andrey and Vladimir Andreevich Markov 3.4 Julian Karol Sochocki 3.5 Konstantin Aleksandrovich Posse 3.6 A. A. Markov’s Lectures 3.7 Résumé Development Outside Russia 4.1 The Mediator: Felix Klein 4.2 Blichfeldt’s Note 4.3 Kirchberger’s Thesis 4.4 Other Non-Quantitative Contributions 4.5 On Convergence and Series Expansions 4.6 Fejér and Runge 4.7 Quantitative Approximation Theory 4.8 Jackson’s Thesis 4.9 A Note About Göttingen’s Role Constructive Function Theory: Kharkiv 5.1 Antony-Bonifatsi Pavlovich Psheborski 5.2 A Short Biography of Sergey Natanovich Bernstein 5.3 First Contributions to Approximation Theory 5.4 Constructive Function Theory as the Development of Chebyshev’s Ideas Biographies... A.1 Matvey Aleksandrovich Tikhomandritski A.2 Nikolaj Yakovlevich Sonin A.3 Aleksandr Vasilevich Vasilev A.4 Ivan Lvovich Ptashitski A.5 Dmitry Fedorovich Selivanov A.6 Aleksandr Mikhaylovich Lyapunov A.7 Ivan Ivanovich Ivanov A.8 Dmitry Alksandrovich Grave A.9 Georgi Feodosievich Voronoy Explanations B.1 Russian Academic Degrees References Index List of Figures List of Tables