Hyperholomorphic functions on commutative algebras

Cauchy theorem for a surface integral in commutative algebras

We prove an analogue of the Cauchy integral theorem for hyperholomorphic functions given in three-dimensional domains with non piece-smooth boundaries and taking values in an arbitrary finite-dimensional commutative associative Banach algebra.

The Cauchy transform in the slice hyperholomorphic setting and related topics

In this paper we study the additive splitting associated to the quaternionic Cauchy transform defined by the Cauchy formula of slice hyperholomorphic functions. Moreover, we introduce and study the analogue of the fundamental solution of the global operator of slice hyperholomorphic functions. We state our results in the quaternionic setting but several results hold for Clifford algebra-valued function with minor changes in the proofs.

The Fock space in the slice hyperholomorphic setting

In this paper we introduce and study some basic properties of the Fock space (also known as Segal-Bargmann space) in the slice hyperholomorphic setting. We discuss both the case of slice regular functions over quaternions and also the case of slice monogenic functions with values in a Clifford algebra. In the specific setting of quaternions, we also introduce the full Fock space. This paper can be seen as the beginning of the study of infinite dimensional analysis in the quaternionic setting.

切片超全纯函数的Corona问题

The Corona Problem for Slice Hyperholomorphic Functions

本文在四元数切片超全纯函数框架下解决了Corona问题，通过将四元数Bezout方程转化为单位圆盘上的方程组，并改编Wolff的证明方法，克服了逐点乘法不封闭的困难。

四元数 $\psi$-超全纯函数的表示

Representation of Quaternionic $ψ$-hyperholomorphic Functions

本文在复数四元数代数中首次引入左、右 $\psi$-超全纯函数，通过过渡到 Cartan 基求解 Cauchy-Fueter 方程，并给出特殊情形下左 $\psi$-超全纯函数的表示。

Convergence of Taylor Series of real normed division algebras

We propose a new way to compute the radius of convergence for Quaternionic hyperholomorphic functions and for Octonion analytic functions. We extend the theorem of Cauchy Hadamard and the theorem of Abel on convergence of series to Quaternionic analysis with the Fueter Operator, to Quaternionic analysis with the Moisil Theodoresco operator and to the Octonion analysis with the Fueter operator.