2 problems

Let $L=-\Delta+|x|^2$ be the Hermite operator on $\mathbb{R}$, and let $h_k$, $k=0,1,2,\ldots$, be the normalized one-dimensional Hermite functions. For $f\in H^1(\mathbb{R})$, wri…

In the one-dimensional Hermite expansion inequality, for $f\in H^1(\mathbb{R})$ one considers bounds of the form … where $\{h_n\}_{n\in\mathbb{N}}$ are the Hermite functions and…