W. Burstein

collaborators

Showing math.CAShow all

4 papers · 1 filter

math.CA2026

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{…

math.CA2025

The Fourier Ratio and complexity of signals

K. Aldaleh, W. Burstein, G. Garza +12

We study the Fourier ratio of a signal $f : Z_{N} \to C$ , \[ \mathrm{FR}(f)\ :=\ \sqrt{N}\,\frac{\|\widehat f\|_{L^1(Î¼)}}{\|\widehat f\|_{L^2(Î¼)}} \ =\ \frac{\|\widehat…

math.CA2025

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…

math.CA2025

$I^_{p}$ Style Bounds in Orlicz Spaces Close to $L^{2}$

Will Burstein

Let $(I ¨ _{i})_{i = 1}^{n}$ be mutually orthogonal functions on a probability space such that $∥ I ¨ _{i} ∥_{\infty} \leq 1$ for all $i \in [n]$ . Let $I^\pm > 0$ . Let $I^¦ (u) = u^{2} lo g^{I^} \pm (u)$ for…

The Fourier Ratio: A Unifying Measure of Complexity for Recovery, Localization, and Learning

The Fourier Ratio and complexity of signals

Fourier minimization and imputation of time series

I^p​ Style Bounds in Orlicz Spaces Close to L2

$I^_{p}$ Style Bounds in Orlicz Spaces Close to $L^{2}$