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Theory of approximation of functions of a real variable

Author: A F Timan; I N Sneddon; S Ulam; M Stark
Publisher: Burlington : Pergamon Press/Elsevier Science, [2014], ©1963.
Series: International series of monographs in pure and applied mathematics, v. 34.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Theory of Approximation of Functions of a Real Variable.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Timan, A.F.
Theory of Approximation of Functions of a Real Variable : International Series of Monographs on Pure and Applied Mathematics.
Burlington : Elsevier Science, ©2014
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: A F Timan; I N Sneddon; S Ulam; M Stark
ISBN: 9781483184814 1483184811
OCLC Number: 898771843
Notes: 4.2. Interpolation formulae for trigonometric polynomials.
Description: 1 online resource (644 pages).
Contents: Front Cover; Theory of Approximation of Functions of a Real Variable; Copyright Page; Table of Contents; EDITORIAL PREFACE; FOREWORD; CHAPTER I. WEIERSTRASS'S THEOREM; 1.1. Approximation of continuous functions by polynomials on a finite segment. The fundamental theorem; 1.2. Proof of Weierstrass's theorem; 1.3. Generalisation and some particular cases. Periodic functions. Functions of many variables; 1.4. Mean approximation of integrable functions by polynomials; 1.5. Some stronger forms of Weierstrass's theorem. 1.6. Approximation of continuous functions on an infinite interval. Uniform approximation by rational functions1.7. Uniform approximation on the whole real axis by integral functions of finite degree; 1.8. On weighted uniform approximation of continuous functions on the whole real axis; 1.9. On mean approximation of integrable functions on an infinite interval; 1.10. Various problems and theorems; CHAPTER II. THE BEST APPROXIMATION; 2.1. The best approximation by polynomials on a finite segment; 2.2. Generalisation to a linear normed space and some particular cases. 2.3. On the uniqueness of the polynomial giving the best uniform approximation. Haar's theorem2.4. On the uniqueness of the polynomial giving the best integral approximation; 2.5. A sequence of best approximations. The fundamental characteristic property; 2.6. The best approximation on an infinite interval; 2.7. Properties of best polynomial approximations. A theorem of Chebyshev; 2.8. On some properties of polynomials of best integral approximations; 2.9. Polynomials which deviate least from zero; 2.10. Estimation of the best approximation. De la Vallée Poussin's theorem. 3.5. Compact classes of differentiable functions3.6. Sets of functions of bounded variation; 3.7. Some classes of functions analytic on a finite segment; 3.8. Some classes of functions analytic on the whole real axis; 3.9. On regularly monotonic functions; 3.10. On quasi-analytic classes of functions; 3.11. Conjugate classes of functions defined on the whole real axis; 3.12. Various problems and theorems; CHAPTER IV. SOME PROPERTIES OF ALGEBRAIC POLYNOMIALS AND TRANSCENDENTAL INTEGRAL FUNCTIONS OF EXPONENTIAL TYPE; 4.1. Interpolation formulae for algebraic polynomials.
Series Title: International series of monographs in pure and applied mathematics, v. 34.
Other Titles: Teorii︠a︡ priblizhenii︠a︡ funkt︠s︡iĭ deĭstvitelʹnogo peremennogo.
Responsibility: A.F. Timan ; translated by J. Berry ; English translation edited and editorial preface by J. Cossar.

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Theory of Approximation of Functions of a Real Variable.

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