Abstract
In the paper we consider a Haar system perturbed in the sense of theL 1(0,1)-metric. We prove that this perturbation is stronger than perturbations in the case of basis stability or stability of complete systems; moreover, the systems obtained as the result of a perturbation are complete inL 1(0,1). An approximation algorithm inL 1(0,1) for these systems is given.
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Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 596–602, October, 1999.
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Filippov, V.I. On strong perturbations of the haar system inL 1(0,1)-space. Math Notes 66, 489–494 (1999). https://doi.org/10.1007/BF02679099
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DOI: https://doi.org/10.1007/BF02679099