论文标题
在某些Bloch-torrey矢量运算符的范围内
On the spectrum of some Bloch-Torrey vector operators
论文作者
论文摘要
我们考虑$ l^2（i，{\ mathbb r}^3）$中的bloch-torrey操作员其中$ i \ subseteq {\ mathbb r} $。与$ l^2（i，{\ mathbb r}^2）$（以及$ l^2（{\ mathbb r}^k，{\ mathbb r}^2）$中的$ l^2（{\ mathbb r}^k，{\ mathbb r}^2）$）。我们获得$ {\ Mathbb r} _+$在$ i = {\ Mathbb r} $的连续频谱中以及实际行之外的离散频谱。对于有限的间隔，我们找到了光谱的左边缘。此外，我们证明Bloch-Torrey操作员必须在$ {\ Mathbb r}^k $中具有相当通用的设置的基本频谱，并为其域找到有效的描述。
We consider the Bloch-Torrey operator in $L^2(I,{\mathbb R}^3)$ where $I\subseteq{\mathbb R}$. In contrast with the $L^2(I,{\mathbb R}^2)$ (as well as the $L^2({\mathbb R}^k,{\mathbb R}^2)$) case considered in previous works. We obtain that ${\mathbb R}_+$ is in the continuous spectrum for $I={\mathbb R}$ as well as discrete spectrum outside the real line. For a finite interval we find the left margin of the spectrum. In addition, we prove that the Bloch-Torrey operator must have an essential spectrum for a rather general setup in ${\mathbb R}^k$, and find an effective description for its domain.
