标题： 整个切片单变量函数上的连续同态的表征 显示英文标题

标题： Characterization of continuous homomorphisms on entire slice monogenic functions

摘要： 本文受到一类在超振荡时间演化中出现的无限阶微分算子的启发。最近，无限阶微分算子已被考虑并在全纯单色函数空间上进行了表征，即位于狄拉克算子核中的函数。本文的重点是表征作用于另一类双正则函数上的无限阶微分算子，这类函数称为取值于克利福德代数的切片双正则函数。我们引入了邻近阶的概念，并建立了全纯双正则函数的一些基本性质，这些性质对于此表征至关重要。 显示英文摘要

摘要： This paper is inspired by a class of infinite order differential operators arising in the time evolution of superoscillations. Recently, infinite order differential operators have been considered and characterized on the spaces of entire monogenic functions, i.e., functions that are in the kernel of the Dirac operators. The focus of this paper is the characterization of infinite order differential operators that act continuously on a different class of hyperholomorphic functions, called slice hyperholomorphic functions with values in a Clifford algebra. We introduce the concept of proximate order and establish some fundamental properties of entire hyperholomorphic functions that are crucial for this characterization.