Limits of Functions and Elliptic Operators

Proceedings Mathematical Sciences

Siddhartha Gadgil¹ 

[1] Stat Math Unit, Indian Statistical Institute, Bangalore 0 0, India$$

关键词: Elliptic regularity;    real-analytic manifolds;    hypoelliptic.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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 $f_n$.

【 授权许可】

Unknown