10 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…
Elliptic curves, Fourier ratio, and sampling complexity
W. Burstein, A. Iosevich, A. Sant
We study the normalized Frobenius trace associated with the Legendre family of elliptic curves over from the point of view of Fourier complexity. If \[ f(t)=\frac{a_p…
Arithmetic functions and learning theory
W. Burstein, A. Iosevich, A. Sant
We establish a connection between analytic number theory and computational learning theory by showing that the Möbius function belongs to a class of functions that is statistically…
The Fourier Ratio: A Unifying Measure of Complexity for Recovery, Localization, and Learning
Will Burstein, Alex Iosevich, Hari Sarang Nathan
We introduce a generalized Fourier ratio, the \(\ell^1/\ell^2\) norm ratio of coefficients in an \emph{arbitrary} orthonormal system, as a single, basis-invariant measure of \emph{…
The Fourier Ratio and complexity of signals
K. Aldaleh, W. Burstein, G. Garza +12
We study the Fourier ratio of a signal , \[ \mathrm{FR}(f)\ :=\ \sqrt{N}\,\frac{\|\widehat f\|_{L^1(μ)}}{\|\widehat f\|_{L^2(μ)}} \ =\ \frac{\|\widehat f…
Fourier minimization and imputation of time series
Will Burstein, Alex Iosevich, Azita Mayeli +1
One of the most common procedures in modern data analytics is filling in missing values in times series. For a variety of reasons, the data provided by clients to obtain a forecast…
Style Bounds in Orlicz Spaces Close to
Will Burstein
Let be mutually orthogonal functions on a probability space such that for all . Let . Let for $u \g…
Group Action Approaches in Erdos Quotient Set Problem
Will Burstein
Let denote the finite field of elements. For , denote the distance set $Δ(E)= \{\|x-y\|^2:=(x_1-y_1)^2+ \cdots + (x_d-y_d)^2 : (x,y)\in…