No minimum rate multisampling of a Fourier series

I examine the possibility of sampling a Fourier series with multiple, uniform rates that are not required to be larger than any particular frequency. This is allowed because convolution of a Fourier series with a train of delta functions in the Fourier domain causes overlap in the Fourier domain only in isolated cases. Furthermore, I can restrict this overlap to not occur in more than one sampled transform. I use three different sampling rates, not required to be greater than any particular frequency, yet satisfying certain irrational relationships, which I specify. The three separate Fourier domains from each rate are compared, and a filter is used which outputs only those terms which are common to all three. In some cases, it might be necessary to introduce a fourth sampling rate. The result is that the original Fourier series is obtained from the filter and inverse transform.