(1) Stat Math Unit, Indian Statistical Institute, 560 059 Bangalore, India
Abstract:
We show that a subspaceS 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 thatS is closed inL2 (M) and that if a sequence of functions fn in ƒn converges inL2(M), then so do the partial derivatives of the functions ƒn.