Gap series and an example to Malliavin's theorem

Robert Kaufman
1969 Pacific Journal of Mathematics  
0. Malliavin's celebrated theorem of spectral nonsynthesis is based on a real function / of class A oo oo f(t) = ^ a n cos nt + Σ δ» sin nt, for which I \u\\\ e iuf ||<»du < oo. J-CO Here and in general 11 g | 1«, = sup % | g(n) |. This note presents a method for constructing a function /, based on a gap property and a method of estimation of Kahane.
doi:10.2140/pjm.1969.28.117 fatcat:nk6vpphe7bbipnxb6eibu4upoe