Geodesic
Relation between approximations in the mean for analytic and for harmonic functions
Matematičeskie zametki, Tome 10 (1971) no. 6, pp. 627-634 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that the completeness of the analytic polynomials always follows from the completeness of the harmonic polynomials in the case of mean-square weighted approximation over a bounded region. 
@article{MZM_1971_10_6_a3,
     author = {F. S. Lisin},
     title = {Relation between approximations in the mean for analytic and for harmonic functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {627--634},
     year = {1971},
     volume = {10},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_6_a3/}
}
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F. S. Lisin. Relation between approximations in the mean for analytic and for harmonic functions. Matematičeskie zametki, Tome 10 (1971) no. 6, pp. 627-634. http://geodesic.mathdoc.fr/item/MZM_1971_10_6_a3/