Conference abstracts
Session A1 - Approximation Theory
No date set
The Beurling-Selberg Box Minorant Problem
Jacob Carruth
University of Texas at Austin, United States - jcarruth@math.utexas.edu
Let $F$ be a function on $\mathbb{R}^d$ which is bandlimited to the unit cube and which minorizes the characteristic function of the unit cube. How large can the integral of $F$ be? Selberg first asked this question to solve a problem in number theory but it has since found many applications including to signal recovery, crystallography, and sphere packing. We show that for a sufficiently large dimensions $d^*$ the answer to this question is zero. Furthermore, we discuss a numerical method which gives an explicit upper bound on $d^*$.
Joint work with Noam Elkies (Harvard University), Felipe Goncalves (University of Alberta) and Michael Kelly (Institute for Defense Analysis, Princeton, NJ).