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Approximation by translates and completeness of weighted systems of exponential functions in \(L^ 2({\mathbb{R}})\). (English. Russian original) Zbl 0569.42001
Math. USSR, Sb. 51, 91-106 (1985); translation from Mat. Sb., Nov. Ser. 123(165), No. 1, 92-107 (1984).
Both necessary conditions and sufficient conditions on a sequence \(\lambda_ n\in {\mathbb{R}}\) are found for the family of translates \(f(t- \lambda_ n)\) of an \(L^ 2\)-function whose Fourier transform is almost everywhere nonzero rapidly decreasing to be dense in \(L^ 2({\mathbb{R}})\).

MSC:
42A10 Trigonometric approximation
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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