论文标题
多切片单基因函数，库奇公式和PS功能演算
Poly slice monogenic functions, Cauchy formulas and the PS-functional calculus
论文作者
论文摘要
自2006年以来，Slice超晶函数的理论和S光谱的相关光谱理论的发展非常快。基于S频谱的新光谱理论在Quaternionic量子力学，在Schur分析和分数扩散问题中的表述中具有应用。在本文中，我们介绍和研究多切片单基因函数的理论，也证明了一些cauchy型积分公式。然后，我们介绍了相关的功能演算，称为PS函数演算，这是S函数演算的多芯片分析版本，它基于S谱的概念。我们研究了微积分的一些不同配方，并证明了其某些特性，其中包括产品规则。
Since 2006 the theory of slice hyperholomorphic functions and the related spectral theory on the S-spectrum have had a very fast development. This new spectral theory based on the S-spectrum has applications, for example, in the formulation of quaternionic quantum mechanics, in Schur analysis and in fractional diffusion problems. In this paper we introduce and study the theory of poly slice monogenic functions, also proving some Cauchy type integral formulas. Then we introduce the associated functional calculus, called PS-functional calculus, which is the polyanalytic version of the S-functional calculus and which is based on the notion of S-spectrum. We study some different formulations of the calculus and we prove some of its properties, among which the product rules.
