Failure of Wiener's property for positive definite periodic functions
| dc.creator | Bonami, Aline | |
| dc.creator | Révész, Szilárd Gy. | |
| dc.date | 2007-11-05 | |
| dc.date.accessioned | 2026-07-07T08:40:45Z | |
| dc.date.available | 2026-07-07T08:40:45Z | |
| dc.description | We say that Wiener's property holds for the exponent $p>0$ if we have that whenever a positive definite function $f$ belongs to $L^p(-ε,ε)$ for some $ε>0$, then $f$ necessarily belongs to $L^p(\TT)$, too. This holds true for $p\in 2\NN$ by a classical result of Wiener. Recently various concentration results were proved for idempotents and positive definite functions on measurable sets on the torus. These new results enable us to prove a sharp version of the failure of Wiener's property for $p\notin 2\NN$. Thus we obtain strong extensions of results of Wainger and Shapiro, who proved the negative answer to Wiener's problem for $p\notin 2\NN$. | |
| dc.identifier | https://arxiv.org/abs/0711.0676 | |
| dc.identifier | http://arxiv.org/abs/0711.0676 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141461 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | Failure of Wiener's property for positive definite periodic functions | |
| dc.type | text |