An Optimization Problem and Point-Evaluation in Paley–Wiener Spaces

Abstract We study the constant $$\mathscr {C}_p$$ C p defined as the smallest constant C such that $$|f(0)|^p \le C\Vert f\Vert _p^p$$ | f ( 0 ) | p ≤ C ‖ f ‖ p p holds for every function f in the Paley–Wiener space $$\text {PW}^p$$ PW p . Brevig, Chirre, Ortega-Cerdà, and Seip have recently shown that $$\mathscr {C}_p C p < p / 2 for all $$p>2$$ p > 2 . We improve this bound for $$2 2 < p ≤ 5 by solving an optimization problem.