标题： 不同函数理论在克利福德分析中的联系 显示英文标题

标题： Connection between Different Function Theories in Clifford Analysis

摘要： 我们描述了方程$Df=0$（广义柯西-黎曼方程）和$(D+M)f=0$的解之间的显式联系，其中算子$D$和$M$可交换。 所描述的联系允许从第一个（广义柯西-黎曼）方程的已知函数理论构造出第二个方程的“函数理论”（柯西定理、柯西积分、泰勒级数和洛朗级数等）。 众所周知，许多与正交旋转群或洛伦兹群相关的物理方程（如狄拉克方程、麦克斯韦方程等）可以自然地用克利福德代数来表述。 对于这些方程，我们的方法给出了零质量（或无外场）和非零质量（或有外场）解之间的显式联系，并提供了一组用于计算的公式。 \keywords{带有质量的狄拉克方程，克利福德分析。} \AMSMSC{30G35}{34L40, 81Q05} 显示英文摘要

摘要： We describe an explicit connection between solutions to equations $Df=0$ (the Generalized Cauchy-Riemann equation) and $(D+M)f=0$, where operators $D$ and $M$ commute. The described connection allows to construct a ``function theory'' (the Cauchy theorem, the Cauchy integral, the Taylor and Laurent series etc.) for solutions of the second equation from the known function theory for solution of the first (generalized Cauchy-Riemann) equation. As well known, many physical equations related to the orthogonal group of rotations or the Lorentz group (the Dirac equation, the Maxwell equation etc.) can be naturally formulated in terms of the Clifford algebra. For them our approach gives an explicit connection between solutions with zero and non-zero mass (or external fields) and provides with a family of formulas for calculations. \keywords{Dirac equation with mass, Clifford analysis.} \AMSMSC{30G35}{34L40, 81Q05}