Piatetski-Shapiro's phenomenon and related problems
| dc.creator | Lev, Nir | |
| dc.date | 2008-07-10 | |
| dc.date.accessioned | 2026-07-07T09:49:35Z | |
| dc.date.available | 2026-07-07T09:49:35Z | |
| dc.description | This Ph.D. thesis, prepared under the supervision of Prof. Alexander Olevskii, is concerned with some problems in two areas of Fourier Analysis: uniqueness theory of trigonometric expansions, and the theory of translation invariant subspaces in function spaces. Our main result in the first area extends to $\ell_q$ spaces ($q > 2$) a deep phenomenon found by Piatetski-Shapiro in 1954 for the space $c_0$. The approach we developed also enabled us to get a result in the second mentioned area, which a priori does not look connected with the first one. The result (maybe, a bit surprising) is: one cannot characterize the functions in $\ell_p(\Z)$ or $L^p(\R)$, $1 < p < 2$, whose translates span the whole space, by the zero set of their Fourier transform. This should be contrasted against the classical Wiener theorems related to the cases $p=1,2$. | |
| dc.description | Ph.D. thesis prepared under the supervision of Professor Alexander Olevskii at Tel-Aviv University (Submitted 2008) | |
| dc.identifier | https://arxiv.org/abs/0807.1628 | |
| dc.identifier | http://arxiv.org/abs/0807.1628 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164640 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42A63 (Primary) 42A65 (Secondary) | |
| dc.title | Piatetski-Shapiro's phenomenon and related problems | |
| dc.type | text |