
02323371
j
1998d.02845
Colzani, Leonardo
An EulerFourier series and the WilbrahamGibbs phenomenon. (Una serie di Eulero  Fourier e il fenomeno di Wilbraham  Gibbs.)
Lett. mat. Pristem, No. 26, 2734 (1997).
1997
Springer, Milano
IT
I35
The author discusses from a mathematical and historical point of view WilbrahamGibbs phenomenon, namely the fact that if we write the Fourier series of any ``reasonable'' locally integrable function, with period $2\pi$, the series converges in every point  but if we take a function with a jump, in a neighbourhood of the discontinuity the partial sums of the Fourier series have fast oscillations and ``miss the target'' by approximately 9\% of the value of the jump.