Talk:Almost periodic function

Quasiperiodic function vs Almost periodic function
Is the link to Quasiperiodic function really necessary? I thought that one was the same as "almost periodic", and I would suggest the redirect from Quasiperiodic function be made to point here, rather than to Quasiperiodic tiling. Suggestions? Oleg Alexandrov 16:15, 13 Feb 2005 (UTC)

PS. I ran into this when considering copying the PlanetMath article quasiperiodic function. Oleg Alexandrov 16:15, 13 Feb 2005 (UTC)

No, they are very different. At least, 'quasiperiodic' has at least two meanings. Charles Matthews 16:36, 13 Feb 2005 (UTC)


 * Got it. One day it might be nice to actually have an article on that. Oleg Alexandrov 17:08, 13 Feb 2005 (UTC)
 * I suggest to put a "not to be confused with" in this article and in the quasi periodic article 79.179.42.44 (talk) 18:59, 18 February 2012 (UTC)

The set of epsilon-periods must be "evenly space" or "relatively dense"
The assertion "He proved that this definition was equivalent to the existence of ε almost-periods, for all ε > 0: that is, translations T(ε) = T of the variable t making |f(t+T)-f(t)|<ε" is wrong.

The correct form is to say that given any positive ε, there exists a positive L(ε) such that for any real x, the interval [x, x+L(ε)] contains an ε almost-period, that is, a τ such that
 * f(t+τ)-f(t)|<ε, for all real t.

Note that if T makes |f(t+T)-f(t)|<ε it is not necessary that |f(t+2*T)-f(t)|<ε, that is, that k*T, k integer, form a set of ε almost-periods, hence the necessity of the L(ε). User:jcpspbr 2006-08-29


 * Made the correction. Acipsen (talk) 14:48, 10 July 2008 (UTC)


 * Interesting & helpful comment, the last phrase could be worth figuring on the main page. BTW, that part of the main page is quite elliptic (e.g., "for all t" is systematically missing ; T(&epsilon;) is misleading since there are many such T, etc.. Of course, once one knows what this section is supposed to explain, it is easily understandable... ;-) &mdash; MFH:Talk 08:38, 29 August 2018 (UTC)

Almost-periodic Operators
See Spectra of Random and Almost-Periodic Operators - "It was the requirements of this theory that motivated the initial study of differential operators with random coefficients in the fifties and sixties, by the physicists Anderson, 1. Lifshitz and Mott ..."