论文标题
通过加权手段对光盘的表征
Characterizations of discs via weighted means
论文作者
论文摘要
证明了在欧几里得平面$ \ rr^2 $中表征分析性光盘的新定理。用于此目的的修改后的Helmholtz方程和谐波功能的加权平均值特性和谐波函数使用。对数重量的存在减少了平均值身份的系数。加权平均值对于Helmholtz方程的解决方案也有效。
New theorems characterizing analytically discs in the Euclidean plane $\RR^2$ are proved. Weighted mean value properties of solutions to the modified Helmholtz equation and harmonic functions are used for this purpose. The presence of a logarithmic weight diminish coefficients in the mean value identities. A weighted mean is also valid for solutions of the Helmholtz equation.
