منابع مشابه
An Approximation by Lacunary Sequence of Vectors
Let (tk)k=0 be a sequence of real numbers satisfying t0 6= 0 and |tk+1| > (1+ 1/M)|tk| for each k > 0, where M > 1 is a fixed number. We prove that for any sequence of real numbers (ξk)k=0 there is a real number ξ such that ||tkξ−ξk|| > 1/(80M log(28M)) for each k > 0. Here, ||x|| denotes the distance from x ∈ R to the nearest integer. This is a corollary derived from our main theorem which is ...
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We obtain a necessary and sufficient condition for the lacunary polynomials to be dense in weighted Lp spaces of functions on the real line. This generalizes the solution to the classical Bernstein problem given by Izumi, Kawata and Hall. © 2005 Elsevier Inc. All rights reserved.
متن کاملApproximation of Continuous Functions by Means of Lacunary Polynomials
be the orthonormal trigonometric sums on Di for weight p(6)cr(0) ; if the u's and v's are uniformly bounded on a point set D2 contained in Di, the same is true of the U's and Vs. For this case the proof admits a materially simpler formulation than when geometric configurations are contemplated having the degree of generality previously considered. The details relating to the loci C', C", K, K',...
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We study the eeects of the use of near-degenerate elements in nite and boundary element methods, and their analogues with mul-tiresolution methods. The main results include: an improved bound for the embedding constant in the Bramble{Hilbert lemma; characterization of the best N-term approximation of solutions of nonlinear operator equations ; best N-term approximation by near-degenerate normal...
متن کاملLacunary Statistical Convergence and Inclusion Properties between Lacunary Methods
A lacunary sequence is an increasing integer sequence θ = {kr } such that kr − kr−1 → ∞ as r → ∞. A sequence x is called sθ-convergent to L provided that for each ε > 0, limr (1/(kr −kr−1)){the number of kr−1 < k ≤ kr : |xk−L| ≥ ε} = 0. In this paper, we study the general description of inclusion between two arbitrary lacunary sequences convergent.
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2009
ISSN: 0019-3577
DOI: 10.1016/s0019-3577(09)80018-9