Original scientific paper

https://doi.org/10.3336/gm.47.2.14

Linear independence and sets of uniqueness

Hrvoje Šikić ; Department of Mathematics, University of Zagreb, Bijenička 30, 10 000 Zagreb, Croatia
Ivana Slamić orcid.org/0000-0002-3284-8052 ; Department of Mathematics, University of Rijeka, Omladinska 14, 51000 Rijeka, Croatia

Abstract

Consider the Bessel system of integer translates {ψk} of a square integrable function ψ. We show that lp-linear independence of {ψk} is equivalent to periodization function pψ(ξ)=∑k Z|(ξ+k)|2 vanishing almost everywhere on a set which is an lp-set of uniqueness, where 1≤ p≤ 2. General result, concerning no restriction on Bessel systems is then proved for the case p=1.

Keywords

Integer translates; l^p-linear independence; sets of uniqueness

Hrčak ID:

93956

URI

https://hrcak.srce.hr/93956

Publication date:

19.12.2012.

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