Geodesic
Splitting entire functions with zeros in a strip
Sbornik. Mathematics, Tome 186 (1995) no. 7, pp. 1071-1084 Cet article a éte moissonné depuis la source Math-Net.Ru

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The following result is proved. If $\varphi$ is a smooth function with support in the interval $[-N, N]$ and if all the zeros of its Fourier transform $$ \widehat\varphi(\lambda)=\int e^{\mathrm i\lambda t}\varphi(t)\,dt $$ are in some horizontal strip, then $\varphi$ can be represented as a convolution of two smooth functions with supports in the interval $[-N/2, N/2]$. 
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R. S. Yulmukhametov. Splitting entire functions with zeros in a strip. Sbornik. Mathematics, Tome 186 (1995) no. 7, pp. 1071-1084. http://geodesic.mathdoc.fr/item/SM_1995_186_7_a8/

[1] Ehrenpreis L., “Solution of some problems of division”, IV, Amer. J. Math., 82 (1960), 522–588 | DOI | MR | Zbl

[2] Demailly J. P., “Construction d'hipersurfaces irreductibles avec lien singulier donne dans $\mathbb C^n$”, Ann. Inst. Fourier, 30:3 (1980), 219–236 | MR | Zbl

[3] Malliavin P., Dixmier J., “Factorisations de functions et de vecteurs indefeniment differentiables”, Bull. Sci. Math., 102:2 (1978), 305–330 | MR | Zbl

[4] Rubel L. A., Squires W. A., Taylor B. A., “Irreducibility of certain entier functions and applications to harmonic analysis”, Annals of Math., 108:2 (1978), 553–567 | DOI | MR | Zbl

[5] Dickson D. G., “Factoring Fourier transforms”, Proceedings of the International Conference on Complex Analysis and its Applications, Varna, 1987

[6] Dickson D. G., “Factoring rapidly decreasing entier functions”, Bull. Sci. Math., 110:2 (1986), 335–345 | MR | Zbl

[7] Dickson D. G., “Factoring functions of exponential type with restriction on a line”, Bull. Sci. Math., 112:2 (1988), 77–100 | MR | Zbl

[8] Dickson D. G., “Factoring Fourier transforms with zeros in a strip”, Proc. Amer. Math. Soc., 106 (1989), 407–414 | DOI | MR

[9] Yulmukhametov R. S., “Approksimatsiya subgarmonicheskikh funktsii”, Analysis Mathematica, 11 (1985), 257–282 | DOI | MR | Zbl