Tempered distributions with discrete support and spectrum

Serhii Favorov

Tempered distributions with discrete support and spectrum

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arxiv 1801.08490 v1 pith:REM2DAPO submitted 2018-01-25 math.CA

Serhii Favorov This is my paper · ORCID

classification math.CA

keywords discretedistributionscountablesupportsupportstemperedconditionsdistribution

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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.

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Pure point measures with sparse support and sparse Fourier--Bohr support
math.MG 2019-08 accept novelty 7.0 of 10

Doubly sparse measures on second countable locally compact Abelian groups are shown to be supported on finitely many translates of a lattice with trigonometric polynomial amplitudes.

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