Wiener-Wintner for Hilbert Transform
| dc.creator | Lacey, Michael | |
| dc.creator | Terwilleger, Erin | |
| dc.date | 2006-01-09 | |
| dc.date.accessioned | 2026-07-07T06:58:41Z | |
| dc.date.available | 2026-07-07T06:58:41Z | |
| dc.description | We prove the following extension of the Wiener--Wintner Theorem in Ergodic Theor and the Carleson Theorem on pointwise convergence of Fourier series: For all measure preserving flows $ (X,μ, T_t)$ and $ f\in L^p (X,μ)$, there is a set $X_f\subset X $ of probability one, so that for all $x\in X_f$ we have \begin{equation*} \lim _{s\downarrow0} \int _{s<\abs t<1/s} \operatorname e ^{i θt} f(\operatorname T_tx)\; \frac{dt}t \qquad \text{exists for all $θ$.} \end{equation*} The proof is by way of establishing an appropriate oscillation inequality which is itself an extension of Carleson's theorem. | |
| dc.description | Submitted to Arkiv | |
| dc.identifier | https://arxiv.org/abs/math/0601192 | |
| dc.identifier | http://arxiv.org/abs/math/0601192 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107453 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Dynamical Systems | |
| dc.title | Wiener-Wintner for Hilbert Transform | |
| dc.type | text |