| Classification and Approximation of Periodic Functions 1995 Edition Contributor(s): Stepanets, A. I. (Author) |
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ISBN: 0792336038 ISBN-13: 9780792336037 Publisher: Springer OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: July 1995 Annotation: This monograph proposes a new classification of periodic functions, based on the concept of generalized derivative, defined by introducing multiplicators and shifts of the argument into the Fourier series of the original function. This approach permits the classification of a wide range of functions, including those of which the Fourier series may diverge in integral metric, smooth functions, and infinitely differentiable functions, including analytical and entire ones. These newly introduced classes are then investigated using the traditional problems of the theory of approximation. The results thus obtained offer a new way to look at classical statements for the approximation of differentiable functions, and suggest possibilities to discover new effects.Audience: valuable reading for experts in the field of mathematical analysis and researchers and graduate students interested in the applications of the theory of approximation and Fourier series. |
| Additional Information |
| BISAC Categories: - Mathematics | Calculus - Mathematics | Mathematical Analysis |
| Dewey: 515.253 |
| LCCN: 95021141 |
| Series: Mathematics and Its Applications |
| Physical Information: 1.06" H x 6.94" W x 9.12" (1.49 lbs) 366 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 (. |