这是一份umass麻省大学 MATH 307作业代写的成功案例
We return to the formulation of the Rjemann Hypothesis given in $\S 3$ above. We consider the differential operator
$$
\left(\frac{1}{2 \pi} \frac{d^{2}}{d X^{2}}+X \frac{d}{d X}+\frac{1}{2}\right)
$$
and its formal adjoint
$$
\left(\frac{1}{2 \pi} \frac{d^{2}}{d X^{2}}-X \frac{d}{d X}+\frac{1}{2}\right)
$$
MATH 307 COURSE NOTES ：
$$
(f, g){0}=\sum{n=1}^{\infty}\left(f, \phi_{n}^{}\right) \overline{\left(g, \phi_{n}\right)} . $$ For $f \in \hat{H}{B^{2}}$, there is an eigen-function expansion $$ f=\sum{n}\left(f, \phi_{n}^{}\right) \phi_{n}
$$
and so the definition is consistent with Parseval’s formula when that is applicable. In particular, we have
$$
|\gamma|_{0}=\sum_{n=1}^{\infty}\left(\gamma, \phi_{n}^{*}\right) \overline{\left(\gamma, \phi_{n}\right)}
$$