منابع مشابه
Gibbs’ Phenomenon and Surface Area
If a function f is of bounded variation on TN (N ≥ 1) and {φn} is a positive approximate identity, we prove that the area of the graph of f ∗φn converges from below to the relaxed area of the graph of f . Moreover we give asymptotic estimates for the area of the graph of the square partial sums of multiple Fourier series of functions with suitable discontinuities.
متن کاملFourier series and the Gibbs phenomenon
An understanding of Fourier series and their generalizations is important for physics and engineering students, as much for mathematical and physical insight as for applications. Students are usually confused by the so-called Gibbs phenomenon-the persistent discrepancy, an "overshoot," between a discontinuous function and its approximation by a Fourier series as the number of terms in the serie...
متن کاملOn the Gibbs Phenomenon and Its Resolution
The nonuniform convergence of the Fourier series for discontinuous functions, and in particular the oscillatory behavior of the finite sum, was already analyzed by Wilbraham in 1848. This was later named the Gibbs phenomenon. This article is a review of the Gibbs phenomenon from a different perspective. The Gibbs phenomenon, as we view it, deals with the issue of recovering point values of a fu...
متن کاملThe Gibbs Phenomenon for Radial Basis Functions
What is now known as the Gibbs phenomenon was first observed in the context of truncated Fourier expansions, but other versions of it arise also in situations such as truncated integral transforms and for different interpolation methods. Radial basis functions (RBF) is a modern interpolation technique which includes both splines and trigonometric interpolations as special cases in 1-D, and it g...
متن کامل2 . Gibbs Phenomenon for Wavelet Sampling Expansions
We deal with the maximum Gibbs ripple of the sampling wavelet series of a discontinuous .function f at a point t ~ R, .for all possible values o.['a satisfying f (t) = ee.f (t 0) + (1 cO.f (t + 0). For the Shannon wavelet series, we make a complete description of all ripples, .for any ot in [0,1]. We show that Meyer sampling series exhibit Gibbs Phenomenon.lor ce < 0 .12495 and ct > 0.306853. W...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2006
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-06-08639-4