Geodesic
Isomorphic type of the space of smooth functions determined by a finite family of differential operators
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 33, Tome 327 (2005), pp. 78-97 Cet article a éte moissonné depuis la source Math-Net.Ru

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On the torus $\mathbb T^n$ with $n\ge 2$, the space mentioned in the title is not isomorphic to a complemented subspace of $C(K)$ if the finite family in question consists of homogeneous differential operators of one and the same order with constant coefficients and at least two among them are linearly independent. 
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S. V. Kislyakov; D. V. Maksimov. Isomorphic type of the space of smooth functions determined by a finite family of differential operators. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 33, Tome 327 (2005), pp. 78-97. http://geodesic.mathdoc.fr/item/ZNSL_2005_327_a5/

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