2008/07/10 by Nir Lev, Lev, Nir
Mathematics · #42A63 (Primary) 42A65 (Secondary) #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics #math.CA #msc:42A63 #msc:42A65
paper · pdf · doi:10.48550/arxiv.0807.1628
Ph.D. thesis prepared under the supervision of Professor Alexander Olevskii at Tel-Aviv University (Submitted 2008)
arxiv created 2008/07/10 · openalex publication_date 2008/07/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ℓq spaces (q > 2) a deep phenomenon found by Piatetski-Shapiro in 1954 for the space c0. 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 ℓp(\Z) or Lp(\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.