离散矩阵值傅里叶乘子的连续统极限
Continuum limit of discretized matrix-valued Fourier multipliers
AI总结：
研究离散矩阵值傅里叶乘子的连续统极限，基于他人成果扩展分析到块算子矩阵，目标是找连续与离散算子预解式差的范数估计，部分离散化方案直接收敛，部分需加校正项。
AI中文摘要：
基于H. Cornean、H. Garde和A. Jensen关于离散狄拉克算子连续统极限的近期结果，我们将分析扩展到一类广泛的块算子矩阵。该类包括双层石墨烯哈密顿量等。我们的主要目标是找到连续算子预解式与其以特定方式嵌入连续统中的离散对应物之间差的范数估计。虽然一些离散化方案在网格参数趋于零时直接导致广义范数预解式意义下的收敛，但其他方案需要添加合适的校正项以确保收敛。
英文摘要：
Building upon a recent result by H. Cornean, H. Garde, and A. Jensen concerning continuum limits of discrete Dirac operators, we extend the analysis to a wide class of block operator matrices. This class includes, among others, the bilayer graphene Hamiltonian. Our main goal is to find norm estimates for the difference between the resolvents of continuous operators and their discrete counterparts embedded in the continuum in a specific way. While some discretization schemes lead directly to convergence in the generalized norm resolvent sense as the mesh parameter tends to zero, others require the addition of a suitable correction term to ensure the convergence.
