Geodesic
Uniform polynomial approximation of entire functions on arbitrary compact sets in the complex plane
Matematičeskie zametki, Tome 58 (1995) no. 3, pp. 355-364

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For an arbitrary compact set $K\subset\mathbb C$, we relate the order and the type of an entire function $f$ to the sequence $E_n(f,H)$ of best polynomial approximations to this function on $K$. 
@article{MZM_1995_58_3_a3,
     author = {A. A. Dovgoshey},
     title = {Uniform polynomial approximation of entire functions on arbitrary compact sets in the complex plane},
     journal = {Matemati\v{c}eskie zametki},
     pages = {355--364},
     publisher = {mathdoc},
     volume = {58},
     number = {3},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_3_a3/}
}
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A. A. Dovgoshey. Uniform polynomial approximation of entire functions on arbitrary compact sets in the complex plane. Matematičeskie zametki, Tome 58 (1995) no. 3, pp. 355-364. http://geodesic.mathdoc.fr/item/MZM_1995_58_3_a3/