Geodesic
Approximation by meromorphic and entire solutions of elliptic equations in Banach spaces of distributions
Sbornik. Mathematics, Tome 189 (1998) no. 4, pp. 481-502

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For a homogeneous elliptic partial differential operator $L$ with constant coefficients and a class of functions (jet-distributions) defined on a closed, not necessarily compact, subset of $\mathbb R^n$ and belonging locally to a Banach space $V$, the approximation in the norm of $V$ of functions in this class by entire and meromorphic solutions of the equation $Lu=0$ is considered. Theorems of Runge, Mergelyan, Roth, and Arakelyan type are established for a wide class of Banach spaces $V$ and operators $L$ they encompass most of the previously considered generalizations of these theorems but also include new results. 
@article{SM_1998_189_4_a0,
     author = {A. Boivin and P. V. Paramonov},
     title = {Approximation by meromorphic and entire solutions of elliptic equations in {Banach} spaces of distributions},
     journal = {Sbornik. Mathematics},
     pages = {481--502},
     publisher = {mathdoc},
     volume = {189},
     number = {4},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_4_a0/}
}
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A. Boivin; P. V. Paramonov. Approximation by meromorphic and entire solutions of elliptic equations in Banach spaces of distributions. Sbornik. Mathematics, Tome 189 (1998) no. 4, pp. 481-502. http://geodesic.mathdoc.fr/item/SM_1998_189_4_a0/