An Optimization Problem and Point-Evaluation in Paley–Wiener Spaces
Abstract
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.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Algebraic and Geometric Analysis
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Constructive Approximation
- Publisher
- Springer Science and Business Media LLC
- Publication date
- 1 September 2026
- Language
- EN