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

Mordechay B. Levin. "A multiparameter variant of the Salem-Zygmund central limit theorem on lacunary trigonometric series." Colloquium Mathematicae 131.1 (2013): 13-27. <http://eudml.org/doc/284260>.

@article{MordechayB2013,
abstract = {We prove the central limit theorem for the multisequence $∑_\{1 ≤ n₁ ≤ N₁\} ⋯ ∑_\{1 ≤ n_d ≤ N_d\} a_\{n₁,...,n_d\} cos(⟨2πm, A₁^\{n₁\}...A_d^\{n_d\}x⟩)$ where $m ∈ ℤ^s$, $a_\{n₁,...,n_d\}$ are reals, $A₁,..., A_d$ 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.},
author = {Mordechay B. Levin},
journal = {Colloquium Mathematicae},
keywords = {central limit theorem; lacunary trigonometric series; partially hyperbolic systems},
language = {eng},
number = {1},
pages = {13-27},
title = {A multiparameter variant of the Salem-Zygmund central limit theorem on lacunary trigonometric series},
url = {http://eudml.org/doc/284260},
volume = {131},
year = {2013},
}

TY - JOUR
AU - Mordechay B. Levin
TI - A multiparameter variant of the Salem-Zygmund central limit theorem on lacunary trigonometric series
JO - Colloquium Mathematicae
PY - 2013
VL - 131
IS - 1
SP - 13
EP - 27
AB - We prove the central limit theorem for the multisequence $∑_{1 ≤ n₁ ≤ N₁} ⋯ ∑_{1 ≤ n_d ≤ N_d} a_{n₁,...,n_d} cos(⟨2πm, A₁^{n₁}...A_d^{n_d}x⟩)$ where $m ∈ ℤ^s$, $a_{n₁,...,n_d}$ are reals, $A₁,..., A_d$ 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.
LA - eng
KW - central limit theorem; lacunary trigonometric series; partially hyperbolic systems
UR - http://eudml.org/doc/284260
ER -