摘要：Let \(\partial_i =\frac{\partial}{\partial x_i}\). The operator \(\partial_i\) is unbounded on \(L^2(\gamma)\). We will explore its adjoint operator \ 阅读全文

摘要：Define on \(\mathbb{R}^d\) the normalized Gaussian measure\[ d \gamma(x)=\frac{1}{(2\pi)^{\frac{d}{2}}} e^{-\frac{|x|^2}{2}}dx\]Consider first the case \(d= 1\). The Taylor expansion of \(e^{-\frac{1}{2}x^2}\) at the point \(x\), with increment \(t\) is \[e^{−\frac{1}{2}(x−t)^2}=\sum_{n=0}^{\infty}a 阅读全文