Characterization of functions with Fourier transform supported on orthants (Q1336163)

The authors give an explicit characterization of the functions in \(L^ p (\mathbb{R}^ n)\) and the distributions in the Schwartz space \(D_{L^ p}' (\mathbb{R}^ n)\), \(1<p<\infty\), whose Fourier transform vanishes on a given number of orthants in \(\mathbb{R}^ n\).