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Limits of functions and elliptic operators. (English) Zbl 1050.58003

Summary: We show that a subspace \(S\) of the space of real analytical functions on a manifold that satisfies certain regularity properties is contained in the set of solutions of a linear elliptic differential equation. The regularity properties are that \(S\) is closed in \(L^2(M)\) and that if a sequence of functions \(f_n\) in \(S\) converges in \(L^2(M)\), then so do the partial derivatives of the functions \(f_n\).

MSC:

58A07 Real-analytic and Nash manifolds
58J05 Elliptic equations on manifolds, general theory
32C07 Real-analytic sets, complex Nash functions
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References:

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