# Strobl18

Harmonic Analysis and Applications

June 4-8, 2018

Strobl, AUSTRIA

### "$l^p(G)$ - linear independence for systems generated by dual integrable representations of LCA groups"

#### Slamic, Ivana

Many important systems in harmonic analysis arise from unitary representations of countable discrete groups, acting on a Hilbert space. If the representation is dual integrable, then the properties of such systems can be described in terms of the associated bracket function. We consider the problem of characterizing l^p(G)- linear independence of such systems in the context of abelian groups, with particular interest in $p\neq 2$ case. The results obtained extend our previous work, concerning integer translates of a square integrable function. Moreover, the approach used in this general setting provides, under certain conditions, a connection with the problem of closure of translates'' in l^p and the problem of existence of p-zero divisors.

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