Poly slice monogenic functions, Cauchy formulas and the PS-functional calculus

The fine structure of the spectral theory on the $S$-spectrum in dimension five

Holomorphic functions play a crucial role in operator theory and the Cauchy formula is a very important tool to define functions of operators. The Fueter-Sce-Qian extension theorem is a two steps procedure to extend holomorphic functions to the hyperholomorphic setting. The first step gives the class of slice hyperholomorphic functions; their Cauchy formula allows to define the so-called $S$-functional calculus for noncommuting operators based on the $S$-spectrum. In the second step this extension procedure generates monogenic functions; the related monogenic functional calculus, based on the …

$S$-谱上多调和与多解析Clifford精细结构的函数与算子

Functions and operators of the polyharmonic and polyanalytic Clifford fine structures on the $S$-spectrum

本文研究$S$-谱上Clifford精细结构中的多调和与多解析函数及其函数演算，并证明单演函数演算与$F$-函数演算等价。

Properties of a polyanalytic functional calculus on the $S$-spectrum

The Fueter mapping theorem gives a constructive way to extend holomorphic functions of one complex variable to monogenic functions, i.e., null solutions of the generalized Cauchy-Riemann operator in $\mathbb{R}^4$, denoted by $\mathcal{D}$. This theorem is divided in two steps. In the first step a holomorphic function is extended to a slice hyperholomorphic function. The Cauchy formula for these type of functions is the starting point of the $S$-functional calculus. In the second step a monogenic function is obtained by applying the Laplace operator in four real variables, namely $ Δ$, to a sl…

逆Fueter定理的一个变体与二阶广义多解析Cauchy-Kovalevskaya延拓

A variation of the inverse Fueter theorem and the generalized polyanalytic Cauchy-Kovalevskaya extension of order 2

本文研究二阶轴向多解析函数的广义Cauchy-Kovalevskaya延拓，建立其与Fueter定理的联系，推导Fueter映射分解的可逆性及相关积分表示公式，是超复分析的重要成果。

The $\mathcal{F}$-resolvent equation and Riesz projectors for the $\mathcal{F}$-functional calculus

The Fueter-Sce-Qian mapping theorem is a two steps procedure to extend holomorphic functions of one complex variable to quaternionic or Clifford algebra-valued functions in the kernel of a suitable generalized Cauchy-Riemann operator. Using the Cauchy formula of slice monogenic functions it is possible to give the Fueter-Sce-Qian extension theorem an integral form and to define the $\mathcal{F}$-functional calculus for $n$-tuples of commuting operators. This functional calculus is defined on the $S$-spectrum but it generates a monogenic functional calculus in the spirit of McIntosh and collabo…

四元数Dirac型精细结构的$H^\infty$-泛函演算

The $H^\infty$-functional calculi for the quaternionic fine structures of Dirac type

本文基于Fueter-Sce扩张定理的积分表示，针对四元数扇形算子构造了四类泛函演算，并利用相应乘积法则建立了它们的$H^\infty$-版本。