Talk:Periodicity condition

Overly restrictive definition
In mathematics and physics, the phrase peridiocity condition has a much broader meaning than the meaning alluded to in this article (as it stands at present). Here are a few examples.
 * In real analysis of a single variable, a "periodicity condition" will generally imply that a function has a real period &tau; – f(x+&tau;) = f(x) for all real x.
 * In complex analysis of a single variable, a "periodicity condition" will generally imply that a function has a complex period &tau; – this in turn implies that the function is some form of the exponential function (which has the period 2&pi;i). Notice that such a function is not necessarily periodic along the real line.
 * Again in complex analysis, a "periodicity condition" might be imposed in two different directions, leading to a doubly-periodic function.
 * In higher dimensional vector spaces, "periodicity conditions" might be imposed in a single dimension, or in more than one dimension, leading to broader or narrower classes of functions satisfying the conditions.
 * In physics, a solution might be periodic in time (this is the particular case to which this article alludes). Again, it could apply to some form of spatial periodicity (as in a standing electromagnetic wave – think of a resonant cavity, or a waveguide).
 * Finally, in a very broad sense, a "periodicity condition" might involve an inequality rather than equality. For example, in the case of a single real variable, the restriction f(x+&tau;) &ge; f(x) might be the "periodicity condition" in a particular context. Or the inequality might be strict, or reversed, etc.

I suppose I could try to fix this article, but I'm too tired right now. I did run a Google Scholar search for the phrase "periodicity condition" -- I got 1,420 hits classified as math, and 2,560 hits classified as physics. Not all of those involve differential equations, either. So I think this article needs to be generalized a lot, if it's going to stay in Wikipedia under this title. DavidCBryant 23:27, 6 August 2007 (UTC)


 * I replaced the article with a redirect to periodic function. That article is much better and in my opinion on the same subject. Feel free to write something along the points mentioned if you ever feel up to it. -- Jitse Niesen (talk) 03:22, 7 August 2007 (UTC)