Limits of functions and elliptic operators

2004/06/28 by Siddhartha Gadgil
Mathematics · #math.DG #msc:58J05 #msc:32C05

paper · pdf

published as Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 2, May 2004, pp. 153-158 · 6 pages, no figures, no tables

arxiv created 2004/06/28 · arxiv updated 2009/12/01

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 L²(M) and that if a sequence of functions f_n in S converges in L²(M), then so do the partial derivatives of the functions f_n.

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