Piatetski-Shapiro's phenomenon and related problems

dc.creatorLev, Nir
dc.date2008-07-10
dc.date.accessioned2026-07-07T09:49:35Z
dc.date.available2026-07-07T09:49:35Z
dc.descriptionThis 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.descriptionPh.D. thesis prepared under the supervision of Professor Alexander Olevskii at Tel-Aviv University (Submitted 2008)
dc.identifierhttps://arxiv.org/abs/0807.1628
dc.identifierhttp://arxiv.org/abs/0807.1628
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/164640
dc.subjectClassical Analysis and ODEs
dc.subject42A63 (Primary) 42A65 (Secondary)
dc.titlePiatetski-Shapiro's phenomenon and related problems
dc.typetext

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