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Limits of functions and elliptic operators

Siddhartha Gadgil
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Abstract

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 $f_n$.

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Siddhartha Gadgil. 2004-06-28. Limits of functions and elliptic operators. https://arxiv.org/abs/math/0406569

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