Gadgil, Siddhartha Limits of functions and elliptic operators. (English) Zbl 1050.58003 Proc. Indian Acad. Sci., Math. Sci. 114, No. 2, 153-158 (2004). 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 Keywords:elliptic regularity; real-analytic manifolds; hypoelliptic PDFBibTeX XMLCite \textit{S. Gadgil}, Proc. Indian Acad. Sci., Math. Sci. 114, No. 2, 153--158 (2004; Zbl 1050.58003) Full Text: DOI arXiv References: [1] Grauert, H., On Levi’s problem and the imbedding of real-analytic manifolds, Ann. Math., 68, 2, 460-472 (1958) · Zbl 0108.07804 · doi:10.2307/1970257 [2] Hörmander, L., The analysis of linear partial differential operators, II, Differential operators with constant coefficients, Grundlehren der Mathematischen Wissenschaften (1983), Berlin: Springer India, Berlin · Zbl 0521.35001 [3] Morrey, C. B., The analytic embedding of abstract real-analytic manifolds, Ann. Math., 68, 2, 159-201 (1958) · Zbl 0090.38401 · doi:10.2307/1970048 [4] Narasimhan, R., Introduction to the theory of analytic spaces, Lect. Notes Math. (1966), Berlin-New York: Springer India, Berlin-New York · Zbl 0168.06003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.