论文标题
第二级和单基因函数的换向代数中的新的Biharmonic基础与Biharmonic方程相关
New biharmonic bases in commutative algebras of the second rank and monogenic functions related to the biharmonic equation
论文作者
论文摘要
在第二级的所有二维通勤代数中，在其所有双谐基础上，$ \ {e_1，e_2 \} $，满足条件$ \ left（e_1^2 + e_2^2^2 \ right）^{2} = 0建立了一组满足Biharmonic方程并在Biharmonic碱产生的实际平面中定义的“分析”（单基因）函数。通过某些单基因函数的实际组成部分，在有限的简单连接域中对Biharmonic函数的表征。
Among all two-dimensional commutative algebras of the second rank a totally of all their biharmonic bases $\{e_1,e_2\}$, satisfying conditions $\left(e_1^2+ e_2^2\right)^{2} = 0$, $e_1^2 + e_2^2 \ne 0$, is found in an explicit form. A set of "analytic" (monogenic) functions satisfying the biharmonic equation and defined in the real planes generated by the biharmonic bases is built. A characterization of biharmonic functions in bounded simply connected domains by real components of some monogenic functions is found.
