Geodesic
On uniform and asymptotic approximation on the real axis by entire functions of restricted growth
Sbornik. Mathematics, Tome 41 (1982) no. 1, pp. 1-32

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This paper establishes results, including both necessary and sufficient conditions, on uniform or asymptotic approximation on the real axis, by entire functions with the slowest possible growth in the complex plane, to arbitrary continuous or continuously differentiable functions, or to functions that are holomorphic in a strip. These results generalize and improve similar results of Bernstein, Keldysh, and others. Bibliography: 20 titles. 
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     author = {N. U. Arakelian},
     title = {On uniform and asymptotic approximation on the real axis by entire functions of restricted growth},
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N. U. Arakelian. On uniform and asymptotic approximation on the real axis by entire functions of restricted growth. Sbornik. Mathematics, Tome 41 (1982) no. 1, pp. 1-32. http://geodesic.mathdoc.fr/item/SM_1982_41_1_a0/