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R. Butler F. Turner† 《International Journal of Mathematical Education in Science & Technology》2013,44(1):33-49
The rate of convergence of a Fourier‐series representation of a given function depends on the nature of the function and of its derivatives. This is shown by using the graphical outputs of a desk computer for different cases. For full‐range series, the effects of continuity and discontinuity of the function and its first derivatives are shown first. The advantage of half‐range formulae due to the free choice of function in the second half‐range are demonstrated next, along with the importance of choice of sine and cosine series according to the function being represented. Finally, a method is given of modifying the given function in a simple manner whereby a dramatic increase in the rate of convergence of the Fourier series is obtained. Examples of the Gibbs overshoot and its elimination are included. 相似文献
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A. S. Belov 《Mathematical Notes》2010,87(3-4):466-474
We prove the sharpness of Zygmund’s theorem, which asserts that if a 2π-periodic function f belongs to L ln+ L, then its Fourier series is convergent in mean. 相似文献
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T. I. Akhobadze 《Analysis Mathematica》1982,8(2):79-102
. , , –1<<0. .
The present work was written on the basis of two earlier works received byAnalysis Mathematica on January 16, 1979, and July 20, 1979. 相似文献
The present work was written on the basis of two earlier works received byAnalysis Mathematica on January 16, 1979, and July 20, 1979. 相似文献
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We establish necessary conditions for the convergence of multiple Fourier series of integrable functions in the mean. 相似文献
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Acta Mathematica Hungarica - 相似文献
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R. A. Avetisyan 《Mathematical Notes》1975,17(4):294-300
In the paper we obtain a formula for the computation of the rectangular partial sums of a double Fourier series of a function of two variables at the point (0, 0), having a discontinuity along any ray at this point. We also give an estimate of the remainder in the abovementioned formula. 相似文献
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S. V. Konyagin 《Proceedings of the Steklov Institute of Mathematics》2009,264(Z1):155-167
Efficient versions of the Cauchy criterion for the convergence in L
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of greedy approximants of trigonometric Fourier series are discussed. 相似文献
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P. V. Zaderei 《Ukrainian Mathematical Journal》1989,41(4):482-487