Perturbations of discrete lattices and almost periodic sets

A discrete set in the $p$-dimensional Euclidian space is {\it almost periodic}, if the measure with the unite masses at points of the set is almost periodic in the weak sense. We propose to construct positive almost periodic discrete sets as an almost periodic perturbation of a full rank discrete lattice. Also we prove that each almost periodic discrete set on the real axes is an almost periodic perturbation of some arithmetic progression. Next, we consider signed almost periodic discrete sets, i.e., when the signed measure with masses $\pm1$ at points of a discrete set is almost periodic. We construct a signed discrete set that is not almost periodic, while the corresponding signed measure is almost periodic in the sense of distributions. Also, we construct a signed almost periodic discrete set such that the measure with masses +1 at all points of the set is not almost periodic.Comment: 6 page

Almost Periodic Discrete Sets

We study the almost periodic discrete sets in R^k. Also, we show the connection between these sets and almost periodic measures and calculate their Fourier transform

On a property of discrete sets in Rk

7-а Міжнародна алгебраїчна конференція в Україні: тези доповідей (18-23 серпня 2009 року, Харків)/ Відп. ред. Г. М. Жолткевич. — Х.: ХНУ им. В.Н. Каразина , 2009. — 168 с. 7th International Algebraic Conference in Ukraine: abstracts of talks (18-23 August, 2009, Kharkov)/ ed. G. N. Zholtkevich. - Kharkov, 2009. - 168 P.У збірнику містяться матеріали Сьомої міжнародної алгебраїчної конференції в Україні, присвяченої 120-річчю від дня народження професора Харківського університету Антона Казиміровича Сушкевича. The collection contains the abstracts of talks of 7th International Algebraic Conference in Ukraine dedicated to the 120th anniversary of Professor of Kharkov University Anton Kazimirovich Sushkevich