Sinossi
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.
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Contenuti
Preface. Introduction. 1. Classes of periodic functions. 2. Integral representations of deviations of linear means of Fourier series. 3. Approximations by Fourier sums in the spaces c and L1. 4. Simultaneous approximation of functions and their derivatives by Fourier sums. 5. Convergence rate of Fourier series and best approximations in the spaces Lp. 6. Best approximations in the spaces C and L. Bibliographical notes. References. Index.
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Classification and Approximation of Periodic Functions (Mathematics and Its Applications, 333)
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Preface. Introduction. 1. Classes of periodic functions. 2. Integral representations of deviations of linear means of Fourier series. 3. Approximations by Fourier sums in the spaces c and L1. 4. Simultaneous approximation of functions and their derivati. Codice articolo 5830850
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Taschenbuch. Condizione: Neu. Classification and Approximation of Periodic Functions | A. I. Stepanets | Taschenbuch | Einband - flex.(Paperback) | Englisch | 2012 | Springer Netherland | EAN 9789401040556 | Verantwortliche Person für die EU: Springer Netherlands, Haberstr. 7, 69126 Heidelberg, buchhandel-buch[at]springer[dot]com | Anbieter: preigu. Codice articolo 105579866
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