论文标题
具有无界扩散项的Schrödinger类型运算符的一般内核估计值
General Kernel estimates of Schrödinger type operators with unbounded diffusion terms
论文作者
论文摘要
我们首先证明了$ a的实现$ a _ {\ min} $ a：= \ mathrm {div}（q \ nabla）-v $ in $ l^2（\ MATHBB {r}^d）$，带有未绑定的系数产生对称的submarkovian和ultraconsemaltive $ l^2（$ l l^2）在$ l^2（\ mathbb {r}^d）\ cap c_b（\ mathbb {r}^d）$上，与通过$ c_b（\ mathbb {r}^d）上的$ a $ a $ a $ a $ a $ a产生的最小半群。此外，使用依赖时间的Lyapunov函数，我们证明了$ a $的热核的上限，并在多项式和指数扩散和潜在系数的情况下推断出$ a _ {\ min} $的某些光谱属性。
We prove first that the realization $A_{\min}$ of $A:=\mathrm{div}(Q\nabla)-V$ in $L^2(\mathbb{R}^d)$ with unbounded coefficients generates a symmetric sub-Markovian and ultracontractive semigroup on $L^2(\mathbb{R}^d)$ which coincides on $L^2(\mathbb{R}^d)\cap C_b(\mathbb{R}^d)$ with the minimal semigroup generated by a realization of $A$ on $C_b(\mathbb{R}^d)$. Moreover, using time dependent Lyapunov functions, we prove pointwise upper bounds for the heat kernel of $A$ and deduce some spectral properties of $A_{\min}$ in the case of polynomially and exponentially diffusion and potential coefficients.
