I believe in Proposition 2, the phrase “where f is in L^2” is not supposed to be there.

Best,

]]>1. In the proof of the first theorem, you write “satisfies the three above properties”, aren’t there just two in the list ?

2. Concerning second condition in the exercise ” ….. $Lf(x) \geq 0$ ” , I am wondering if it should be replaced by $Lf(x) \leq 0$, which is consistent with the statement of Th\’eor\`eme 0.1 of the paper by courr\`ege.

Best, luc

]]>More knowledge seems to be required.

Thank you. ]]>

In lecture 6 you will use this theorem in the case of H=L^2_\mu(R^n,R), the real Hilbert space.

But In many books I have ever seen the famous theorem is treated only in complex Hilbert spaces, not real. Is it also true in the real case? ]]>