Almost sure invariance principles for lacunary trigonometric series
نویسندگان
چکیده
منابع مشابه
Lacunary Trigonometric Series. Ii
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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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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ژورنال
عنوان ژورنال: Comptes Rendus de l'Académie des Sciences - Series I - Mathematics
سال: 2001
ISSN: 0764-4442
DOI: 10.1016/s0764-4442(01)01913-9