Abstract
The paper is devoted to the study of completeness problem of systems {ϕ n (x)} =0 ∞ inL σ (a, b), where −∞≦a<b≦+∞,δ(x) is a weight function subject to mild assumptions, andϕ(x) is a continuous function on (a,b), either bounded or unbounded in the neighbourhood of the end-points of (a,b). It turns out that this problem is connected with that of quasianalyticity of certain additive set of functions at a given point. As the most important application of the general results, the completeness problem is treated for systems of orthogonal polynomials.
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