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

Tom 131 / 2013

Mordechay B. Levin Colloquium Mathematicum 131 (2013), 13-27 MSC: Primary 60F15; Secondary 42A55, 42B. DOI: 10.4064/cm131-1-2

Streszczenie

We prove the central limit theorem for the multisequence $$ \sum_{1 \leq n_1 \leq N_1} \cdots \sum_{1 \leq n_d \leq N_d} a_{n_1, \ldots ,n_d} \cos (\langle 2\pi \mathbf{m}, A_1^{n_1} \dots A_d^{n_d} \mathbf{x} \rangle) $$ where $\mathbf{m} \in \mathbb Z^s$, $a_{n_1, \ldots ,n_d}$ are reals, $A_1, \ldots ,A_d$ are partially hyperbolic commuting $s\times s$ matrices, and $\mathbf{x}$ is a uniformly distributed random variable in $[0,1]^s$. The main tool is the S-unit theorem.

Autorzy

  • Mordechay B. LevinDepartment of Mathematics
    Bar-Ilan University
    Ramat-Gan, 5290002, Israel
    e-mail

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