Geodesic
Joint Approximations of Distributions in Banach Spaces
Matematičeskie zametki, Tome 73 (2003) no. 2, pp. 179-194

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For a given homogeneous elliptic partial differential operator $L$ with constant complex coefficients, two Banach spaces $V_1$ and $V_2$ of distributions in $\mathbb R^N$, and compact sets $X_1$ and $X_2$ in $\mathbb R^N$, we study joint approximations in the norms of the spaces $V_1(X_1)$ and $V_2(X_2)$ (the spaces of Whitney jet-distributions) by the solutions of the equation $L_u=0$ in neighborhoods of the set $X_1\cup X_2$. We obtain a localization theorem, which, under certain conditions, allows one to reduce the above-cited approximation problem to the corresponding separate problems in each of the spaces. 
@article{MZM_2003_73_2_a2,
     author = {A. M. Voroncov},
     title = {Joint {Approximations} of {Distributions} in {Banach} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {179--194},
     publisher = {mathdoc},
     volume = {73},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_73_2_a2/}
}
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A. M. Voroncov. Joint Approximations of Distributions in Banach Spaces. Matematičeskie zametki, Tome 73 (2003) no. 2, pp. 179-194. http://geodesic.mathdoc.fr/item/MZM_2003_73_2_a2/