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

100%

Levin M.

Colloquium Mathematicum

2013

tom 131

nr 1

13-27

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.

Explicit construction of normal lattice configurations

63%

Levin M., Smorodinsky M.

Colloquium Mathematicum

2005

tom 102

nr 1

33-47

We extend Champernowne's construction of normal numbers to base b to the $ℤ^{d}$ case and obtain an explicit construction of a generic point of the $ℤ^{d}$ shift transformation of the set ${0,1,...,b-1}^{ℤ^{d}}$.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Levin M.

1 Smorodinsky M.

1 2013

1 2005

Wyniki wyszukiwania

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

Explicit construction of normal lattice configurations