We investigate properties of tempered distributions with discrete or countable supports such that their Fourier transforms are distributions with discrete or countable supports as well. We find sufficient conditions for support of the distribution to be a finite union of translations of a full-rank lattice.
Necessary and sufficient conditions for differentiability of a function of several variables
Quasicrystals with discrete support and spectrum
Necessary and sufficient conditions for a function involving divided differences of the di- and tri-gamma functions to be completely monotonic
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