On Three Balls Theorem for Discrete Harmonic Functions
On Three Balls Theorem for Discrete Harmonic Functions
复制标题
关于离散调和函数的三球定理
DOI：
10.1007/s40315-014-0076-9
复制
发表时间：
2014
影响因子：
2.1
通讯作者：
E. Malinnikova
中科院分区：
文献类型：
--
作者：
Maru Guadie;E. Malinnikova
给出了一个初等论证，证明了$${\mathbb {R}}^n$$ Rn中连续调和函数的三球定理，该定理适用于晶格上离散调和函数的情况。我们得到的三球定理的离散模拟包含一个额外的项，它取决于网格的网格大小，当网格大小为零时，它也趋于零。我们还证明了立方体上的任何离散调和函数与该立方体上的离散调和多项式重合。
We give an elementary argument to prove the Three Balls Theorem for continuous harmonic functions in $${\mathbb {R}}^n$$Rn which can be adapted to the case of discrete harmonic functions on the lattice. The discrete analog of the Three Balls Theorem that we obtain contains an additional term that depends on the mesh size of the lattice and goes to zero when the mesh size goes to zero. We also show that any discrete harmonic function on a cube coincides with a discrete harmonic polynomial on this cube.