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

Is it true that since the smooth forms are dense in the $L^2$ and $H^{1,2}$ sections of forms, we can extend the exterior derivative $d$ and its adjoint $d^*$ to this spaces?

share|cite|improve this question
Can you extend the usual derivative from $C^\infty(\mathbb R)$ to $L^2(\mathbb R)$? – Mariano Suárez-Alvarez Aug 19 '12 at 18:59
$d$ is continuous so I would define it as $d(f)=\lim d(\psi_n )$ where $\psi_n \rightarrow f$ , $f \in L^2$ $\psi_n in C^\infty$ – inquisitor Aug 19 '12 at 19:38
$d$ is continuous with respect to what topology on $C^\infty$? Why would the limit you are proposing to use as definition exist? – Mariano Suárez-Alvarez Aug 19 '12 at 19:40
@MarianoSuárez-Alvarez: $H^{1,2}$ is the space of functions with one square integrable derivative. Why do you unsettle the OP like that? As a side remark: your first comment, in my opinion, should read: can you extend the usual derivative to $H^{1,2}$ – user20266 Aug 19 '12 at 20:07
This answer might be relevant. – user31373 Aug 19 '12 at 20:42

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.