Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

For elliptic differential operators $P$ on a compact manifold $M$, we have the formula

$$\mathrm{ind}(D) = \mathrm{tr}(e^{-tP^*P}) - \mathrm{tr}(e^{-tPP^{\star}})$$

I would think that this holds for Pseudo-Differential operators of positive order as well, but no text book states that. Is it not true? If not, what goes wrong?

share|improve this question
You only need $P$ to be an elliptic ps.d.o. on a compact manifold. –  Liviu Nicolaescu Oct 7 '12 at 15:14
Ok, two things that I keep forgetting to mention. Thank you! –  Kofi Oct 7 '12 at 23:31
add comment

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.