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An Approximation by Lacunary Sequence of Vectors
Published online by Cambridge University Press: 01 May 2008
Abstract
Let be a sequence of real numbers satisfying for each k ≥ 0, where M ≥ 1 is a fixed number. We prove that, for any sequence of real numbers , there is a real number ξ such that for each k ≥ 0. Here, denotes the distance from to the nearest integer. This is a corollary derived from our main theorem, which is a more general matrix version of this statement with explicit constants.
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- Copyright © Cambridge University Press 2008
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