Reuben Wheeler

activity

20202024

collaborators

5 papers

math.CA2024

Variation bounds for spherical averages over restricted dilates

Reuben Wheeler

We study $L^{p} \to L^{q} (V_{E}^{r})$ variation semi-norm estimates for the spherical averaging operator, where $E \subset [1, 2]$ .

math.NT2023

Fourier Dimension Estimates for Sets of Exact Approximation Order: The Badly-Approximable Case

Robert Fraser, Reuben Wheeler

We show for decreasing, positive approximation functions $ψ$ such that $τ = lim_{q \to \infty} \frac{l o g ψ ( q )}{l o g q} < \frac{13 + 73}{8}$ and such that $q^{2} ψ (q) \to 0$ t…

math.CA2022

Root structures of polynomials with sparse exponents

Reuben Wheeler

For real polynomials with (sparse) exponents in some fixed set, \[ Ψ(t)=x+y_1t^{k_1}+\ldots +y_L t^{k_L}, \] we analyse the types of root structures that might occur as the coeffic…

math.NT2021

Fourier Dimension Estimates for Sets of Exact Approximation Order: the Well-Approximable Case

Robert Fraser, Reuben Wheeler

We obtain a Fourier dimension estimate for sets of exact approximation order introduced by Bugeaud for certain approximation functions $ψ$ . This Fourier dimension estimate implies…

math.CA2020

A note on the $L^{p}$ integrability of a class of Bôchner-Riesz kernels

Reuben Wheeler

For a general compact variety $Γ$ of arbitrary codimension, one can consider the $L^{p}$ mapping properties of the Bôchner-Riesz multiplier $$ m_{Γ, α}(ζ) \ = \ {\rm dist}(ζ, Γ)^α ϕ(…

Variation bounds for spherical averages over restricted dilates

Fourier Dimension Estimates for Sets of Exact Approximation Order: The Badly-Approximable Case

Root structures of polynomials with sparse exponents

Fourier Dimension Estimates for Sets of Exact Approximation Order: the Well-Approximable Case

A note on the Lp integrability of a class of Bôchner-Riesz kernels

A note on the $L^{p}$ integrability of a class of Bôchner-Riesz kernels