On evil Kronecker sequences and lacunary trigonometric products
نویسندگان
چکیده
منابع مشابه
On Lacunary Trigonometric Series.
1. Fundamental theorem. In a recent paper f I have proved the theorem that if a lacunary trigonometric series CO (1) X(a* cos nk6 + bk sin nk9) (nk+x/nk > q > 1, 0 ^ 0 ^ 2ir) 4-1 has its partial sums uniformly bounded on a set of 0 of positive measure, then the series (2) ¿(a*2 + bk2) k-l converges. The proof was based on the following lemma (which was not stated explicitly but is contained in ...
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where E c [0, 1] is any given set o f positive measure and {ak} any given sequence of real numbers. This theorem was first proved by R. Salem and A. Zygmund in case of a -0, where {flk} satisfies the so-called Hadamard's gap condition (cf. [4], (5.5), pp. 264-268). In that case they also remarked that under the hypothesis (1.2) the condition (1.3) is necessary for the validity of (1.5) (cf. [4]...
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The purpose of this paper is to define and study the spaces [ĉ,M, p](∆u , q, s), [ĉ,M, p, ] θ 0(∆ m u , q, s) and [ĉ,M, p, ] θ ∞(∆ m u , q, s) of lacunary convergent sequences. We also study some inclusion relations between these spaces and some properties and theorems. 2000 Mathematics Subject Classification:40D05, 40A05. 1.Introduction and definitions Let w denote the set of all complex seque...
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x (1.2) lim I {t; t e E, SN(t) < xAN} / I E _ (2~r)-1/2 exp( u2/2)du. *' Recently, it is proved that the lacunarity condition (1.1) can be relaxed in some cases (c.f. [1] and [4]). But in [1] it is pointed out that to every constant c>0, there exists a sequence {nk} for which nk+l > nk(1 + ck--1(2) but (1.2) is not true for ak =1 and E_ [0, 11. The purpose of the present note is to prove the fo...
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Recursive constructions are given which permit, under conditions described in the paper, a (v, b, r, k, lambda)configuration to be used to obtain a (v', b', r', k, lambda)-configuration. Although there are many equivalent definitions we will mean by a (v, b, r, k, lambda)-configuration or BIBD that (0, 1)-matrix A of size v x b with row sum r and column sum k satisfying AAT = (r lambda)I + lamb...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2017
ISSN: 0373-0956,1777-5310
DOI: 10.5802/aif.3094