Geodesic
Fourier--Laplace transformation of functionals on a~weighted space of infinitely smooth functions on~$\mathbb R^n$
Sbornik. Mathematics, Tome 195 (2004) no. 10, pp. 1477-1501

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The dual of the space of infinitely smooth functions on $\mathbb R^n$ with partial derivatives satisfying certain weighted estimates is described in terms of the Fourier–Laplace transformation. An integral representation is obtained for the solutions of a homogeneous linear partial differential equation with constant coefficients that belong to this space. 
@article{SM_2004_195_10_a3,
     author = {I. Kh. Musin},
     title = {Fourier--Laplace transformation of functionals on a~weighted space of infinitely smooth functions on~$\mathbb R^n$},
     journal = {Sbornik. Mathematics},
     pages = {1477--1501},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2004_195_10_a3/}
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I. Kh. Musin. Fourier--Laplace transformation of functionals on a~weighted space of infinitely smooth functions on~$\mathbb R^n$. Sbornik. Mathematics, Tome 195 (2004) no. 10, pp. 1477-1501. http://geodesic.mathdoc.fr/item/SM_2004_195_10_a3/