Conference abstracts

Session A1 - Approximation Theory

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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).

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