On Gröchenig, Heil, and Walnut's proof of the local three squares theorem
The main result says the following. Consider strictly positive numbers \(r_2> r_1\) for which \(r_1/r_2 \notin Q\), and let \(\mu_k\) denote the characteristic function for the interval \([-r_k,r_k]\). Then the set of functions of the form \((g_1 \mu_1)*\mu_2+ \mu_1*(g_2\mu_2)\) with \(g_1,g_2\in L^2(-(r_1+r_2),r_1+r_2)\) is dense in \(L^2(-(r_1+r_2),r_1+r_2)\). A \(d\)-dimensional version is obtained by convolution.
scientific article; zbMATH DE number 1928892