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An Approximation by Lacunary Sequence of Vectors

Published online by Cambridge University Press:  01 May 2008

ARTŪRAS DUBICKAS
ARTŪRAS DUBICKAS*
Affiliation:
Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius LT-03225, Lithuania; Institute of Mathematics and Informatics, Akademijos 4, LT-08663 Vilnius, Lithuania (e-mail: arturas.dubickas@mif.vu.lt)
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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.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 3 , May 2008 , pp. 339 - 345
Copyright
Copyright © Cambridge University Press 2008

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