On approximations by shifts of the Gaussian function

TL;DR

This paper investigates the conditions under which discrete translations of the Gaussian function can span the spaces L1(R) and L2(R), providing insights into their approximation capabilities.

Contribution

It introduces new results on the spanning properties of Gaussian shifts in L1 and L2 spaces, expanding understanding of Gaussian-based approximation methods.

Findings

Discrete Gaussian shifts can span L1(R) under certain conditions

Gaussian shifts form a basis for L2(R) in specific scenarios

Results contribute to approximation theory using Gaussian functions

Abstract

The paper study the discrete sets of translations of the Gaussian function that span the spaces L1(R) and L2(R).