Uniqueness theorem for Fourier transformable measures on LCA groups

  • S.Yu. Favorov Karazin National University of Kharkiv
Keywords: Fourier transformable measure; discrete support; almost periodic measure

Abstract

We show that if points of supports of two discrete ”not very thick” Fourier transformable measures on locally compact abelian (LCA) groups tend to one another at infinity and the same is true for the masses at these points, then these measures coincide. The result is valid for discrete almost periodic measures on LCA groups too. Also, we show that the result is false for some discrete ”thick” measures. To do this, we construct a discrete almost periodic measure on the real axis, whose masses at the points of support tend to zero as these points approach infinity.

Author Biography

S.Yu. Favorov, Karazin National University of Kharkiv

Kharkiv National University, Svobody sq, 4, faculty of mechanics and mathematics

References

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Published
2020-12-25
How to Cite
1.
Favorov S. Uniqueness theorem for Fourier transformable measures on LCA groups. Mat. Stud. [Internet]. 2020Dec.25 [cited 2021Dec.9];54(2):211-9. Available from: http://matstud.org.ua/ojs/index.php/matstud/article/view/162
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Articles