Simon Baker

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20212025

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math.DS2025

On the Fourier transform of random Bernoulli convolutions

Simon Baker, Henna Koivusalo, Sascha Troscheit +1

We investigate random Bernoulli convolutions, namely, probability measures given by the infinite convolution \[ μ_ω= \mathop{\circledast}_{k=1}^{\infty} \left( \frac{δ_0 + δ_{λ_1 λ…

math.DS2025

On finitely many base $q$ expansions

Simon Baker, George Bender

Given some integer $m \geq 3$ , we find the first explicit collection of countably many intervals in $(1, 2)$ such that for any $q$ in one of these intervals, the set of points with…

math.DS2024

Fourier Decay from $L^{2}$ -Flattening

Simon Baker, Osama Khalil, Tuomas Sahlsten

We develop a unified approach for establishing rates of decay for the Fourier transform of a wide class of dynamically defined measures. Among the key features of the method is the…

math.DS2023

On the cardinality and dimension of the slices of Okamoto's functions

Simon Baker, George Bender

The graphs of Okamoto's functions, denoted by $K_{q}$ , are self-affine fractal curves contained in $[0, 1]^{2}$ , parameterised by $q \in (1, 2)$ . In this paper we consider the cardinalit…

math.DS2021

On normal numbers and self-similar measures

Amir Algom, Simon Baker, Pablo Shmerkin

Let ${f_{i} (x) = s_{i} \cdot x + t_{i}}$ be a self-similar IFS on $R$ and let $β > 1$ be a Pisot number. We prove that if $\frac{l o g ∣ s _{i} ∣}{l o g β} \in / Q$ fo…

On the Fourier transform of random Bernoulli convolutions

On finitely many base q expansions

Fourier Decay from L2-Flattening

On the cardinality and dimension of the slices of Okamoto's functions

On normal numbers and self-similar measures

On finitely many base $q$ expansions

Fourier Decay from $L^{2}$ -Flattening