A multiparameter variant of the Salem-Zygmund central limit theorem on lacunary trigonometric series

Mordechay B. Levin

Colloquium Mathematicae, Tome 131 (2013), p. 13-27 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove the central limit theorem for the multisequence $\sum_{1 \leq n ₁ \leq N ₁} \dots \sum_{1 \leq n_{d} \leq N_{d}} a_{n ₁, . . ., n_{d}} c o s (⟨ 2 π m, A ₁^{n ₁} . . . A_{d}^{n_{d}} x ⟩)$ where $m \in ℤ^{s}$ , $a_{n ₁, . . ., n_{d}}$ are reals, $A ₁, . . ., A_{d}$ are partially hyperbolic commuting s × s matrices, and x is a uniformly distributed random variable in ${[0, 1]}^{s}$ . The main tool is the S-unit theorem.

Publié le : 2013-01-01

Zbl 1279.60040

EUDML-ID : urn:eudml:doc:284260

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     author = {Mordechay B. Levin},
     title = {A multiparameter variant of the Salem-Zygmund central limit theorem on lacunary trigonometric series},
     journal = {Colloquium Mathematicae},
     volume = {131},
     year = {2013},
     pages = {13-27},
     zbl = {1279.60040},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm131-1-2}
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Mordechay B. Levin. A multiparameter variant of the Salem-Zygmund central limit theorem on lacunary trigonometric series. Colloquium Mathematicae, Tome 131 (2013) pp. 13-27. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm131-1-2/