Completeness of Certain Exponential Systems and Zeros of Lacunary Polynomials
Abstract
Let be a subset of \0,1,2,...\. We show that if has `gaps' then the completeness and frame properties of the system \tke2π i nt: n∈Z,k∈\ differ from those of the classical exponential systems. This phenomenon is closely connected with the existence of certain uniqueness sets for lacunary polynomials.
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