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

• Autorzy: Mordechay B. Levin
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42A55: Lacunary series of trigonometric and other functions; Riesz products
• 60F15: Strong theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 131
• Numer: 1
• Strony: 13-27

Daty

wydano

2013

Twórcy

autor

Mordechay B. Levin

• Department of Mathematics, Bar-Ilan University, Ramat-Gan, 5290002, Israel

Identyfikatory

DOI

10.4064/cm131-1-2