Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

If $f_i$ are real analytic functions on $\mathbb R^n$ such that for arbitrary partial derivative index $\alpha \ge 0$, $f_i^\alpha \to {f^\alpha }$ uniformly, is it necessary that $f$ is an analytic function?

share|cite|improve this question
You say that $\alpha$ is just an index (and I guess, not a power) - then I wail to find how is is used in your statement. – Ilya Dec 6 '11 at 11:41
Are you using $f^{\alpha}$ as notation for a partial derivative of $f$ of arbitrary order? If not, I, too, am puzzled as to how to understand your notation. – Gerry Myerson Dec 6 '11 at 11:50
Sorry for the unclarity, I have clarified it. – Hezudao Dec 6 '11 at 12:04
In mathoverflow this question was discussed.… – bonnnnn2010 Dec 6 '11 at 13:29

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.