Approximation by meromorphic and entire solutions of elliptic equations in Banach spaces of distributions

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 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.