$R^n$空间中的Cauchy积分公式

In this note p(D) = Dm+ b1Dm 1+···+ bmis a polynomial Dirac operator in R~n, where D =nj=1ej xjis a standard Dirac operator in Rn, bjare the complex constant coefficients. In this note we discuss all decompositions of p(D) according to its coefficients bj,and obtain the corresponding explicit Cauchy integral formulae of f which are the solution of p(D)f = 0.

Cauchy Integral Formulae in $\mathbb{R}^n$

In this note $p(\underline{D})={\underline{D}}^m+b_1{\underline{D}}^{m-1}+\cdots+b_m$ is a polynomial Dirac operator in $\mathbb{R}^n$, where $\underline{D}=\sum^n_{j=1} e_j\frac{\partial }{\partial x_j}$ is a standard Dirac operator in $\mathbb{R}^n$, $b_j$ are the complex constant coefficients. In this note we discuss all decompositions of $p(\underline{D})$ according to its coefficients $b_j$, and obtain the corresponding explicit Cauchy integral formulae of $f$ which are the solution of $p(\underline{D})f=0$.