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Journal of the London Mathematical Society 2001 63(2):428-440; doi:10.1017/S0024610700001782
© 2001 by London Mathematical Society
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© The London Mathematical Society

Sparse Systems of Functions Closed on Large Sets in RN

Alexander Ulanovskii

Høgskolen i Stavanger PO Boks 2557 Ullandhaug, Stavanger 4404, Norway, Alexander.Ulanovskii{at}tn.his.no

Received 21 July 1999. Revision received 19 May 2000.

Let E(Z) = {einx}nisinZ denote the trigonometrical exponential system. It is well known that E(Z) forms an orthogonal basis in the space L2(0, 2{pi}). In 1964, H. Landau discovered that the trigonometrical system has the following property: certain small perturbations of E(Z) yield exponential systems which are complete in L2 on any finite union of 2{pi}-periodic translations of any interval ({varepsilon}, 2{pi}–{varepsilon}), 0 < {varepsilon} < {pi}.


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