与双边单演函数有关的Vegua型系统

Riemann-Hilbert problems for axially symmetric monogenic functions in $\mathbb{R}^{n+1}$

We focus on the Clifford-algebra valued variable coefficients Riemann-Hilbert boundary value problems $\big{(}$for short RHBVPs$\big{)}$ for axially monogenic functions on Euclidean space $\mathbb{R}^{n+1},n\in \mathbb{N}$. With the help of Vekua system, we first make one-to-one correspondence between the RHBVPs considered in axial domains and the RHBVPs of generalized analytic function on complex plane. Subsequently, we use it to solve the former problems, by obtaining the solutions and solvable conditions of the latter problems, so that we naturally get solutions to the corresponding Schwarz…

切片单演函数理论中的广义Π算子及其应用

Generalized Π-operator in the theory of slice monogenic functions and applications

本文在切片单演函数理论中引入广义Π算子，研究其映射性质、左右逆及伴随算子，并应用于切片Beltrami方程，证明其范数估计决定方程解的存在性。

On two-sided monogenic functions of axial type

In this paper we study two-sided (left and right) axially symmetric solutions of a generalized Cauchy-Riemann operator. We present three methods to obtain special solutions: via the Cauchy-Kowalevski extension theorem, via plane wave integrals and Funk-Hecke's formula and via primitivation. Each of these methods is effective enough to generate all the polynomial solutions.

A Cauchy kernel for the Hermitian submonogenic system

Hermitian monogenic functions are the null solutions of two complex Dirac type operators. The system of these complex Dirac operators is overdetermined and may be reduced to constraints for the Cauchy datum together with what we called the Hermitian submonogenic system (see [8],[9]). This last system is no longer overdetermined and it has properties that are similar to those of the standard Dirac operator in Euclidean space, such as a Cauchy-Kowalevski extension theorem and Vekua type solutions. In this paper, we investigate plane wave solutions of the Hermitian submonogenic system, leading to…