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math.CA2026
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…
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{…