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# Classification and Approximation of Periodic Functions

### Mathematics and Its Applications

Hardcover Published: 31st July 1995
ISBN: 9780792336037
Number Of Pages: 366

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The chapters are split into sections, which, in turn, are split into subsections enumerated by two numbers: the first stands for the number of the section while the second for the number ofthe subsection itself. The same numeration is used for all kinds of statements and formulas. If we refer to statements or formulas in other chapters, we use triple numeration where the first number stands for the chapter and the other two have the same sense. The results presented in this book were discussed on the seminars at the Institute of Mathematics of Ukrainian Academy ofSciences, at the Steklov Mathematical Institute of the Academy of Sciences of the USSR, at Moscow and Tbilisi State Universities. I am deeply grateful to the heads of these seminars Professors V. K. Dzyadyk, N. P. Kor- neichuk, S. B. Stechkin, P. L. U1yanov, and L. V. Zhizhiashvili as well as to the mem- bers ofthese seminars that took an active part in the discussions. In TRODUCTIon It is well known for many years that every 21t -periodic summable function f(x) can be associated in a one-to-one manner with its Fourier series (1. 1) Slfl where I It = - f f(t)cosktdt 1t -It and I It - f f(t)sinktdt. 1t -It Therefore, if for approximation of a given function f(*), it is necessary to construct a sequence ofpolynomials Pn (.

 Preface Introduction p. 1 Classes of Periodic Functions p. 5 Integral Representations of Deviations of Linear Means of Fourier Series p. 43 Approximations by Fourier Sums in the Spaces C and L[subscript 1] p. 81 Simultaneous Approximation of Functions and their Derivatives by Fourier Sums p. 209 Convergence Rate of Fourier Series and Best Approximations in the Spaces L[subscript p] p. 255 Best Approximations in the Spaces C and L p. 305 Bibliographical Notes p. 347 References p. 351 Index p. 359 Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792336037
ISBN-10: 0792336038
Series: Mathematics and Its Applications
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 366
Published: 31st July 1995
Publisher: SPRINGER VERLAG GMBH
Country of Publication: NL
Dimensions (cm): 23.17 x 17.63  x 2.69
Weight (kg): 0.68

Earn 496 Qantas Points
on this Book