تقرير
Point evaluation in Paley--Wiener spaces
| العنوان: | Point evaluation in Paley--Wiener spaces |
|---|---|
| المؤلفون: | Brevig, Ole Fredrik, Chirre, Andrés, Ortega-Cerdà, Joaquim, Seip, Kristian |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Classical Analysis and ODEs, Mathematics - Complex Variables, Mathematics - Functional Analysis |
| الوصف: | We study the norm of point evaluation at the origin in the Paley--Wiener space $PW^p$ for $0 < p < \infty$, i. e., we search for the smallest positive constant $C$, called $\mathscr{C}_p$, such that the inequality $|f(0)|^p \leq C \|f\|_p^p$ holds for every $f$ in $PW^p$. We present evidence and prove several results supporting the following monotonicity conjecture: The function $p\mapsto \mathscr{C}_p/p$ is strictly decreasing on the half-line $(0,\infty)$. Our main result implies that $\mathscr{C}_p p/2$ for $1 \leq p < 2$. We also estimate the asymptotic behavior of $\mathscr{C}_p$ as $p \to \infty$ and as $p \to 0^+$. Our approach is based on expressing $\mathscr{C}_p$ as the solution of an extremal problem. Extremal functions exist for all $0 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2210.13922 |
| رقم الأكسشن: | edsarx.2210.13922 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |