# Poisson Formula and Orthonormality

Please see the attached file for the fully formatted problems.

4. "Poisson Formula and Orthonormality".

Let .... be the Fourier transform of (x)

.....

With the Poisson formula one can show that the family of functions ......

is orthonormal if and only if

..... = const.

PROVE or DISPROVE this claim. If the claim is true, what would be the value of "const."?

https://brainmass.com/math/geometry-and-topology/poisson-formula-orthonormality-17684

#### Solution Preview

Please see the attachment.

Proof:

Assume , , . Let

Then we can ...

#### Solution Summary

Orthonormality of a Fourier transform is proven using the Poisson formula. The slution is detailed and well presented.

$2.19