lokofer
Aug25-06, 01:14 PM
If we have (Poisson sum formula) in the form:
\sum_{n=-\infty}^{\infty}f(n)= \int_{-\infty}^{\infty}dx f(x) \omega (x)
with \omega (x) = \sum_{n=-\infty}^{\infty}e^{2i \pi nx}
Then my question is if we would have that:
\sum_{n=-\infty}^{\infty} \frac{ f(n)}{ \omega (n)} = \int_{-\infty}^{\infty} dx f(x) ??
\sum_{n=-\infty}^{\infty}f(n)= \int_{-\infty}^{\infty}dx f(x) \omega (x)
with \omega (x) = \sum_{n=-\infty}^{\infty}e^{2i \pi nx}
Then my question is if we would have that:
\sum_{n=-\infty}^{\infty} \frac{ f(n)}{ \omega (n)} = \int_{-\infty}^{\infty} dx f(x) ??