Poisson type generators for L^1(R)

TL;DR

This paper characterizes specific discrete sets on the real line that allow certain functions with Poisson-like Fourier transforms to generate the entire L^1(R) space through translation.

Contribution

It provides a new characterization of discrete sets enabling translation-generated spans in L^1(R) for functions with Poisson-like Fourier transforms.

Findings

Identifies conditions on discrete sets for spanning L^1(R)

Links Fourier transform behavior to translation spans

Advances understanding of Poisson-type generators

Abstract

We characterize the discrete sets L of the real line such that {f(t-l), l in L} span L^1(R), f being an L^1(R)-function whose Fourier transform behaves like the one of the Poisson function.