Sedletskij, A. M. 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 \(L^ 2({\mathbb{R}})\). Cited in 1 Review MSC: 42A10 Trigonometric approximation 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type Keywords:translates; Fourier transform PDFBibTeX XMLCite \textit{A. M. Sedletskij}, Math. USSR, Sb. 51, 91--106 (1985; Zbl 0569.42001); translation from Mat. Sb., Nov. Ser. 123(165), No. 1, 92--107 (1984) Full Text: DOI