- #1
reterty
- 29
- 2
As is well known, almost periodic functions can be represented as a Fourier series with incommensurable (non-multiple) frequencies https://en.wikipedia.org/wiki/Almost_periodic_function. It seems to me that I came up with an integral criterion for the degree of non-periodicity. The integral of a periodic function (not including the constant component of its Fourier series), with respect to the argument for the main period, is equal to zero. In the theory of almost periodic functions, the concept of an almost period is introduced. So, a similar integral of an almost periodic function for almost a period will be different from zero. Its value divided by this almost period and the largest of the amplitudes of the harmonics of the Fourier series will be a dimensionless quantity characterizing the degree of non-periodicity of this almost periodic function. Is my criterion correct and useful?