This question arises from a Fourier transform class I took about a year back.
The poisson summation formula is:
$$\displaystyle \sum_{n= - \infty}^{\infty} f(n) = \displaystyle \sum_{k= - \infty}^{\infty} \hat{f}(k)$$
where $\hat{f}$ is the Fourier Transform of $f(x)$.
It is interesting since this is true for all $f(x)$ for which we can define Fourier transform.
Is there a nice (probably physical) interpretation for this?
I am wondering if this characterizes some property which is invariant, some sort of conservation.
For instance, if we consider Parseval's theorem, one interpretation of it is that the total energy across all time is the total energy across all of its frequency components.
Also, from a mathematical standpoint what does this mean? Is this a manifestation of some property of integers?