Functions with time and frequency gaps
The purpose of this note is to give an explicit and straightforward construction of functions in \(L^1\cap C^\infty(\mathbb{R})\) that have prescribed gaps around the origin in both time and frequency domain. These gaps can be chosen independently and of arbitrary size. Moreover, the construction shows that the subspace of functions with these support properties is infinite-dimensional. An interesting additional feature of some examples is that they have periodic zero sets on both the time and the frequency domain.
scientific article; zbMATH DE number 1019266