As promised in my last blog post, I am writing this post to briefly explain the main ideas of the proof of the main Theorem in my paper about Landau’s necessary density conditions for the Hankel transform.

Recall that, given a function defined in we define its Hankel transform as

where is the Bessel function of order .

We want to understand how dense sampling or interpolation sequences have to be. Let’s say our objective is to understand how many points a sampling sequence has to have on an interval .

Continue reading Proof of Landau’s conditions for the Hankel transform