关于Appell集与Fueter-Sce映射

Generalized Appell polynomials and Fueter-Bargmann transforms in the polyanalytic setting

Tnis paper deals with some special integral transforms in the setting of quaternionic valued slice polyanalytic functions. In particular, using the polyanalytic Fueter mappings it is possible to construct a new family of polynomials which are called the generalized Appell polynomials. Furthermore, the range of the polyanalytic Fueter mappings on two different polyanalytic Fock spaces is characterized. Finally, we study the polyanalytic Fueter-Bargmann transforms.

Fock and Hardy spaces: Clifford-Appell case

In this paper, we study a specific system of Clifford-Appell polynomials and in particular their product. Moreover, we introduce a new family of quaternionic reproducing kernel Hilbert spaces in the framework of Fueter regular functions. The construction is based on a general idea which allows to obtain various function spaces, by specifying a suitable sequence of real numbers. We focus on the Fock and Hardy cases in this setting, and we study the action of the Fueter mapping and its range.

Fueter-Sce映射与Clifford-Appell多项式

The Fueter-Sce mapping and the Clifford-Appell polynomials

本文利用Fueter-Sce映射与广义Cauchy-Kovalevskaya延拓的联系，显式计算其作用并刻画值域与核，定义新乘积，研究相关空间，并推广得到高维多解析单演多项式。

On a sequence of monogenic polynomials satisfying the Appell condition whose first term is a non-constant function

In this paper we aim at constructing a sequence $\{\mathsf{M}_n^k(x)\}_{n\ge0}$ of $\mathbb R_{0,m}$-valued polynomials which are monogenic in $\mathbb R^{m+1}$ satisfying the Appell condition (i.e. the hypercomplex derivative of each polynomial in the sequence equals, up to a multiplicative constant, its preceding term) but whose first term $\mathsf{M}_0^k(x)=\mathbf{P}_k(\underline x)$ is a $\mathbb R_{0,m}$-valued homogeneous monogenic polynomial in $\mathbb R^m$ of degree $k$ and not a constant like in the classical case. The connection of this sequence with the so-called Fueter's theorem …

On the connection between the Fueter-Sce-Qian theorem and the generalized CK-extension

The Fueter-Sce-Qian theorem provides a way of inducing axial monogenic functions in $\mathbb{R}^{m+1}$ from holomorphic intrinsic functions of one complex variable. This result was initially proved by Fueter and Sce for the cases where the dimension $m$ is odd using pointwise differentiation, while the extension to the cases where $m$ is even was proved by Qian using the corresponding Fourier multipliers. In this paper, we provide an alternative description of the Fueter-Sce-Qian theorem in terms of the generalized CK-extension. The latter characterizes axial null solutions of the Cauchy-Riema…

一个超复变量中的流形富特 - 谢现象

A manifold Fueter-Sce phenomenon in one hypercomplex variable

研究将富特 - 谢现象置于强\(T\)正则函数类背景下，发现该现象出现在一般结合\(*\)代数上，其对称性是多轴的，且富特等人研究的现象是多步骤过程最后一步，发现超复变量新现象。