Alexander Olevskii

Completeness in L2(ℝ) of almost integer translates

Abstract We prove that for any noninteger real sequence λ n = n + o (1), there exists a function φL 2 (ℝ) such that the system of translates φ ( t — λ n ) spans all of the space L 2 (ℝ) .

Quasicrystals and Poisson’s summation formula

We characterize the measures on

Wiener's 'closure of translates' problem and Piatetski-Shapiro's uniqueness phenomenon

\mathbb {R}

Fourier quasicrystals and discreteness of the diffraction spectrum

R which have both their support and spectrum uniformly discrete. A similar result is obtained in

On the prediction problem

\mathbb {R}^n

Singular Distributions and Symmetry of the Spectrum

Rn for positive measures.