11 papers
Pointwise Convergence of Random Ergodic Averages at the \(L^1\) Endpoint
Will Burstein, Lorenzo Catani, Ben Krause
In his highly influential paper, \emph{On the maximal ergodic theorem for certain subsets of the integers}, Bourgain introduced the study of pointwise convergence of ergodic averag…
Fourier Ratio and Restricted Isometry via Entropic Descent
Will Burstein, W. Burstein, Alex Iosevich +3
In this second paper on descent methods as proof mechanisms in harmonic analysis (the first treated Bourgain's selection theorem), entropic mirror descent gives an improved…
Bourgain's Lambda(p) selection theorem: a greedy proof with polynomial failure bounds
Will Burstein, Alex Iosevich, Ben Krause
We give a self-contained proof of Bourgain's finite selection theorem with an explicit probability bound. For every and , given pairwise orthogonal function…
Endpoint Estimates for Stein's Purely Quadratic Carleson Operator
Anastasios Fragkos, Ben Krause, Michael Lacey
We study the near behavior of the maximally quadratically modulated Hilbert transform \[ \mathcal{C}_2f(x) := \sup_λ \left|\operatorname{p.v.} \int_{\mathbb{R}}f(x-y)e^{2 πi…
Quantitative bounds for sets lacking polynomial progressions with shifted prime difference
Ben Krause, Hamed Mousavi, Terence Tao +1
We prove quantitative polynomial Szemerédi-type theorems involving polynomial progressions with shift parameter restricted to the set of shifted primes . The types of…
Pointwise Convergence of Ergodic Averages Along Integer Cantor Sets
Félix Brokering Pinilla, Alex Iosevich, Ben Krause
Let , \[ D \subsetneq \{ 0,1,\dots,d-1\}, \qquad |D| \geq 2, \ 0 \in D \] be a finite alphabet, and define the integer Cantor set \begin{align} \mathcal{C} := \mathcal{C}…
A Variation Norm Carleson Theorem Along the Primes
Anastasios Fragkos, Ben Krause, Nazar Miheisi +1
Let denote the von Mangoldt function; we prove that for each , there exist constants \[ r' < \mathbf{c}(r) < 2 < \mathbf{C}(r), \qquad \lim_{r \to \infty} \mathbf{c}(r)…
Benchmarking Scientific Machine Learning Models for Air Quality Data
Khawja Imran Masud, Venkata Sai Rahul Unnam, Sahara Ali
Accurate air quality index (AQI) forecasting is essential for the protecting public health in rapidly growing urban regions, and the practical model evaluation and selection are of…
The Wiener Wintner Theorem Along the Primes
Jan Fornal, Anastasios Fragkos, Ben Krause +3
We prove the following Wiener-Wintner Theorem along the sequence of prime times, the first extension of the Wiener-Wintner Theorem to arithmetic sequences: for every probability sp…
Cross representations of additive complements of -th powers
Yuchen Ding, Ben Krause, Csaba Sándor +2
Let be the set of natural numbers and the set of -th powers, where is a natural number. Let $\mathcal{W}_r…
An Approach To Endpoint Problems in Oscillatory Singular Integrals
Alex Iosevich, Ben Krause, Hamed Mousavi
In this note we provide a quick proof that maximal truncations of oscillatory singular integrals are bounded from to . The methods we us…