Re: Riemann-Lebseque lemma and rate of convergence
- From: David C. Ullrich <ullrich@xxxxxxxxxxxxxxxx>
- Date: Wed, 18 May 2005 06:14:33 -0500
On 17 May 2005 22:40:44 -0700, bryant_j_j@xxxxxxxxx wrote:
>howdy all,
>
> the classical riemann-lebseque lemma tell us that the fourier series
>coefficients of a continuous or piecewise continuous function on
>[-\pi,pi], say F, tends to zero as n-> oo. however, are there any
>bounds on the rate of convergence to zero of the fourier coefficients?
As Robert said, no, not without more assumptions.
A general theme in Fourier analysis is that smoothness of a function
corresponds to rapid decay of the coefficients - there are many
specific results in this direction.
>relevant references would be appreciated. TIA.
************************
David C. Ullrich
.
- References:
- Riemann-Lebseque lemma and rate of convergence
- From: bryant_j_j
- Riemann-Lebseque lemma and rate of convergence
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