论文标题
n Quathnionic分析中的N规范功能
n-Regular Functions in Quaternionic Analysis
论文作者
论文摘要
在本文中，我们研究了最初在[FL4]中引入的左右N规范功能。当n = 1时，这些函数是通常的Quaternionic左右常规功能。我们表明，N规范函数满足了通常的常规函数的大多数属性，包括保形组和Cauchy-Fueter型繁殖公式下的分数线性转换下的共形不变性。可以说的是，这些n型函数的这些cauchy-fueter型复制公式是cauchy的Quaternionic类似物，用于n-ther阶杆的积分公式，表达了全体形函数的（n-1）-St衍生物。 We also find two expansions of the Cauchy-Fueter kernel for n-regular functions in terms of certain basis functions, we give an analogue of Laurent series expansion for n-regular functions, we construct an invariant pairing between left and right n-regular functions and we describe the irreducible representations associated to the spaces of left and right n-regular functions of the conformal group and its Lie algebra.
In this paper we study left and right n-regular functions that originally were introduced in [FL4]. When n=1, these functions are the usual quaternionic left and right regular functions. We show that n-regular functions satisfy most of the properties of the usual regular functions, including the conformal invariance under the fractional linear transformations by the conformal group and the Cauchy-Fueter type reproducing formulas. Arguably, these Cauchy-Fueter type reproducing formulas for n-regular functions are quaternionic analogues of Cauchy's integral formula for the n-th order pole expressing the (n-1)-st derivative of a holomorphic function. We also find two expansions of the Cauchy-Fueter kernel for n-regular functions in terms of certain basis functions, we give an analogue of Laurent series expansion for n-regular functions, we construct an invariant pairing between left and right n-regular functions and we describe the irreducible representations associated to the spaces of left and right n-regular functions of the conformal group and its Lie algebra.
