论文标题
无限图上的schrödinger和多谐操作员：抛物线范围内的光谱和p独立性
Schrödinger and polyharmonic operators on infinite graphs: Parabolic well-posedness and p-independence of spectra
论文作者
论文摘要
我们分析了由Schrödinger运算符生成的半群的属性$-Δ+V $或多谐操作员$ - （ - δ）^m $，在$ l^p $ - 空格和连续功能的空间上的公制图上。在空间恒定电势的情况下，我们为其内核提供了半阐释公式。在图表上的额外的亚指数生长条件下，我们证明了这些半群的分析性，超包性和尖端的内核估计。我们还表明，它们的发电机的光谱在所有相关功能空间上重合，并呈现kre \uın型维度的降低，表明它们的频谱值取决于作用于组合图上支持的各种功能空间的广义离散拉普拉斯人的光谱。
We analyze properties of semigroups generated by Schrödinger operators $-Δ+V$ or polyharmonic operators $-(-Δ)^m$, on metric graphs both on $L^p$-spaces and spaces of continuous functions. In the case of spatially constant potentials, we provide a semi-explicit formula for their kernel. Under an additional sub-exponential growth condition on the graph, we prove analyticity, ultracontractivity, and pointwise kernel estimates for these semigroups; we also show that their generators' spectra coincide on all relevant function spaces and present a Kre\uın-type dimension reduction, showing that their spectral values are determined by the spectra of generalized discrete Laplacians acting on various spaces of functions supported on combinatorial graphs.
