The Gibbs-Wilbraham phenomenon: An episode in fourier analysis

  title={The Gibbs-Wilbraham phenomenon: An episode in fourier analysis},
  author={Edwin Shields Hewitt and Robert E. Hewitt},
  journal={Archive for History of Exact Sciences},
plays an essential r61e in computing the amount of this overshoot. While teaching a course in the theory of functions of a real variable, E. HEWITT found the value 1.71... listed for the integral (1) in HARDY & ROGOSINSKI [271, page 36. This anomaly, as well as others encountered in the literature, led us to a study of the GIBBS phenomenon and its history. In the course of this study we uncovered a maze of forgotten results, interesting and difficult generalizations, faulty constants, and some… 

A Review of David Gottlieb's Work on the Resolution of the Gibbs Phenomenon

Givena piecewise smooth function, it is possible toconstruct a global expan- sion in some complete orthogonal basis, such as the Fourier basis. However, the local discontinuities of the function will

On the Gibbs Phenomenon and Its Resolution

The Gibbs phenomenon is reviewed from a different perspective and it is shown that the knowledge of the expansion coefficients is sufficient for obtaining the point values of a piecewise smooth function, with the same order of accuracy as in the smooth case.

Pointwise fourier inversion in several variables

This report outlines some recent developments in Fourier analysis which can be discussed using only elementary calculus of several variables.

A Stability Barrier for Reconstructions from Fourier Samples

It is proved that any stable method for resolving the Gibbs phenomenon can converge at best root-exponentially fast in $m$ and any method with faster convergence must also be unstable, and in particular, exponential convergence implies exponential ill-conditioning.

Mapped polynomials and discontinuous kernels for Runge and Gibbs phenomena

In this paper, we present recent solutions to the problem of approximating functions by polynomials for reducing in a substantial manner two well-known phenomena: Runge and Gibbs. The main idea is to


An n-dimensional manifold (or, more briefly, an n-manifold) is a space that locally looks like n-dimensional Euclidean space Rn . Manifolds are thus the n-dimensional generalizations of nonsingular

Filters, mollifiers and the computation of the Gibbs phenomenon

  • E. Tadmor
  • Mathematics, Computer Science
    Acta Numerica
  • 2007
The aim in the computation of the Gibbs phenomenon is to detect edges and to reconstruct piecewise smooth functions, while regaining the high accuracy encoded in the spectral data.

A Fourier continuation framework for high-order approximations

It is well known that approximation of functions on $[0,1]$ whose periodic extension is not continuous fail to converge uniformly due to rapid Gibbs oscillations near the boundary. Among several



Note on Gibbs' phenomenon

In my review of the third edition of volume I of Picard's Traité d'Analyse,* I took exception to Picard's claim that Du Bois-Keymond had discovered Gibbs' phenomenon. Concerning the question of

Introduction to the theory of Fourier's series and integrals

fold, of plane, and of line, tha t are present within an ' eventful ' fourfold—a fourfold whose absolute is associated with the equation x+y + z — i =0—is complete and valuable. I t is typical of the

Introduction to the Theory of Fourier's Series and Integrals

PROF. CARSLAW'S excellent book is so well known that it needs little general introduction. The first edition, published in 1906, was a work on “Fourier's Series and Integrals and the Mathematical

A historical note on Gibbs’ phenomenon in Fourier’s series and integrals

for the Fourier's series which represents f{x) = x in the interval —TV < x < TV, fall from the point (—n, 0) at a steep gradient to a point very nearly at a depth 2j0 [(sin a) Ia] da below the axis

Fourier's Series

FOURIER'S series arises in the attempt to express, by an infinite series of sines (and cosines) of multiples of x, a function of x which has given values in an interval, say from x = − π to x = π.

Fourier's Series

I SHOULD like to add a few words concerning the subject of Prof. Michelson's letter in NATURE of October 6. In the only reply which I have seen (NATURE, October 13), the point of view of Prof.

Handbook of Mathematical Functions with Formulas, Graphs,

The DLMF, also being published as a book, is the successor to Abramowitz and Stegun's NBS Handbook of Mathematical Functions with Formulas, Graphs. Handbook of Mathematical Functions has 24 ratings

A Note Upon Phosphorescent Earthworms

The regularity, and the mode of excitation, of the luminosity seems to show that Microscolex is phosphorescent in its own right.

Fourier's Series

IN all expositions of Fourier's series which have come to my notice, it is expressly stated that the series can represent a discontinuous function.

Über die Bestimmung des Sprunges der Funktion aus ihrer Fourierreihe.

ist konvergent, und ihr Grenzwert ist '— 0 •^°"~— . & Dieses Dirichletsche Theorem gibt eine Methode, nach welcher man aus der Fourierreihe von f(x) das arithmetische Mittel der beiden zur