Glasnik Matematicki, Vol. 47, No. 2 (2012), 415-420.

LINEAR INDEPENDENCE AND SETS OF UNIQUENESS

Hrvoje Šikić and Ivana Slamić

Department of Mathematics, University of Zagreb, Bijenička 30, 10 000 Zagreb, Croatia
e-mail: hsikic@math.hr

Department of Mathematics, University of Rijeka, Omladinska 14, 51000 Rijeka, Croatia
e-mail: islamic@math.uniri.hr

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.

2010 Mathematics Subject Classification.   42C15, 46E30.

Key words and phrases.   Integer translates, lp-linear independence, sets of uniqueness.

Full text (PDF) (free access)

DOI: 10.3336/gm.47.2.14

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