论文标题
离散的傅立叶乘数的规范分辨率融合
Norm resolvent convergence of discretized Fourier multipliers
论文作者
论文摘要
我们证明了使用生物息肉riesz序列嵌入连续体中的运算符及其离散对应物的分解差异的规范估计。这些估计值在操作员的正方形集成函数上的操作员规范中给出，并明确取决于离散操作员的网格大小。操作员是傅立叶乘数和乘法电位的总和。傅立叶乘数包括分数laplacian和伪忠实的自由汉密尔顿人。电势是真实的，有界的，并且连续hölder。作为副产品，连续和离散算子的分解和离散操作员的光谱之间的距离在网格尺寸中与标准分辨率估计值相同。原始操作员在当地的Hausdorff距离处的光谱也相同。
We prove norm estimates for the difference of resolvents of operators and their discrete counterparts, embedded into the continuum using biorthogonal Riesz sequences. The estimates are given in the operator norm for operators on square integrable functions, and depend explicitly on the mesh size for the discrete operators. The operators are a sum of a Fourier multiplier and a multiplicative potential. The Fourier multipliers include the fractional Laplacian and the pseudo-relativistic free Hamiltonian. The potentials are real, bounded, and Hölder continuous. As a side-product, the Hausdorff distance between the spectra of the resolvents of the continuous and discrete operators decays with the same rate in the mesh size as for the norm resolvent estimates. The same result holds for the spectra of the original operators in a local Hausdorff distance.
