论文标题
部分可观测时空混沌系统的无模型预测
Discrete approximations to Dirichlet and Neumann Laplacians on a half-space and norm resolvent convergence
论文作者
论文摘要
我们将laplacian在$ \ mathbf {r}^d $中的离散近似的结果扩展到具有标准分解收敛的最新结果，并在半空间上向Dirichlet和Neumann Laplacians的相应结果。离散的Dirichlet/Neumann Laplacians的分解被嵌入连续体中，并使用自然离散化和嵌入操作员嵌入。正常分辨率的融合与连续的对应物已被证明，在网格尺寸中具有二次速率。这些结果以有限的速度概括，还包括具有真实，有界和霍尔德持续潜力的运营商，以及Dirichlet/Neumann Laplacians的某些功能，包括任何积极的实际力量。 注意（2024年11月27日）：PDF末尾已添加了一个折面。
We extend recent results on discrete approximations of the Laplacian in $\mathbf{R}^d$ with norm resolvent convergence to the corresponding results for Dirichlet and Neumann Laplacians on a half-space. The resolvents of the discrete Dirichlet/Neumann Laplacians are embedded into the continuum using natural discretization and embedding operators. Norm resolvent convergence to their continuous counterparts is proven with a quadratic rate in the mesh size. These results generalize with a limited rate to also include operators with a real, bounded, and Hölder continuous potential, as well as certain functions of the Dirichlet/Neumann Laplacians, including any positive real power. Note (Nov 27, 2024): A corrigendum has been added to the end of the PDF.
