Geodesic
Approximation by translates and completeness of weighted systems of exponential functions in $L^2(\mathbf R)$
Sbornik. Mathematics, Tome 51 (1985) no. 1, pp. 91-106 
A. M. Sedletskii. Approximation by translates and completeness of weighted systems of exponential functions in $L^2(\mathbf R)$. Sbornik. Mathematics, Tome 51 (1985) no. 1, pp. 91-106. http://geodesic.mathdoc.fr/item/SM_1985_51_1_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Both necessary conditions and sufficient conditions on a sequence $\lambda_n\in\mathbf R$ are found for the family of translates $f(t-\lambda_n)$ of an $L^2$-function whose Fourier transform is almost everywhere nonzero and rapidly decreasing to be dense in $L^2(\mathbf R)$. Bibliography: 9 titles.

[1] Viner N., Integral Fure i nekotorye ego prilozheniya, Fizmatgiz, M., 1963

[2] Faxen B., “On approximation by translates and related problems in function theory”, Ark. math., 19:2 (1981), 271–289 | DOI | MR | Zbl

[3] Zalik R., “On some gap theorems and the closure of translates”, Notic. Amer. Math. Soc., 25:2 (1978), A-314

[4] Zalik R., “On approximation by shifts and a theorem of Wiener”, Trans. Amer. Math. Soc., 243 (1978), 299–308 | DOI | MR | Zbl

[5] Babenko K. I., “Ob odnoi novoi probleme kvazianalitichnosti i o preobrazovanii Fure tselykh funktsii”, Trudy Mosk. matem. ob-va, 1956, no. 5, 523–542 | MR | Zbl

[6] Evgrafov M. A., Asimptoticheskie otsenki i tselye funktsii, Nauka, M., 1979 | MR | Zbl

[7] Mandelbroit S., Ryady Dirikhle. Printsipy i metody, Mir, M., 1973 | Zbl

[8] Levin B. Ya., Raspredelenie kornei tselykh funktsii, Gostekhizdat, M., 1956

[9] Boas R. P., Entire functions, Acad. press, N.Y., 1954 | MR | Zbl