A subgroup H of R is characterized if H=tau_R:={x in R: u_n x --> 0 mod Z} for some sequence u in R. Given two sequences u and v in R, we find conditions under which tau_u(R) is contained or not in tau_v(R). As a by-product of our main theorems, we find a known result by Elias on inclusions of characterized subgroups of T, motivated by problems in harmonic analysis.
Inclusions of characterized subgroups
BARBIERI, Giuseppina Gerarda;
2017
Abstract
A subgroup H of R is characterized if H=tau_R:={x in R: u_n x --> 0 mod Z} for some sequence u in R. Given two sequences u and v in R, we find conditions under which tau_u(R) is contained or not in tau_v(R). As a by-product of our main theorems, we find a known result by Elias on inclusions of characterized subgroups of T, motivated by problems in harmonic analysis.File in questo prodotto:
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