Bump Functions With Monotone Fourier Transforms Satisfying Decay Bounds
arXiv:2003.12364 · doi:10.1016/j.jat.2022.105742
Abstract
The existence of a smooth, nonnegative, compactly supported function with monotone (on the half-line) Fourier transform satisfying two-sided decay bounds is demonstrated.
7 pages, 1 figure; the main result is strengthened by requiring the constructed function to be nonnegative