论文标题
无限级差分差分运算符，作用于整个超晶函数
Infinite order differential operators acting on entire hyperholomorphic functions
论文作者
论文摘要
无限顺序差异运算符出现在数学和物理学的不同领域，在过去的几十年中，他们在研究超激动的发展中至关重要，这是Schrödinger方程的初始基准。受量子力学出现的操作员的启发，在本文中，我们研究了作用于整个超晶函数空间的一类无限阶差分算子的连续性。 Fueter-SCE-QIAN映射定理说明了两类的超晶函数，构成对Paravector变量函数的自然函数的自然扩展。我们表明，即使多形函数的两个概念彼此差异很大，但整个超晶型函数的指数界限在无限顺序差异操作员的连续性中起着至关重要的作用。我们指出一个了不起的事实，即Paravector变量的指数函数不在Dirac运算符的内核中，而是具有指数界限的整个单基因函数在理论中起着重要作用。
Infinite order differential operators appear in different fields of Mathematics and Physics and in the last decades they turned out to be of fundamental importance in the study of the evolution of superoscillations as initial datum for Schrödinger equation. Inspired by the operators arising in quantum mechanics, in this paper we investigate the continuity of a class of infinite order differential operators acting on spaces of entire hyperholomorphic functions. The two classes of hyperholomorphic functions, that constitute a natural extension of functions ofone complex variable to functions of paravector variables are illustrated by the Fueter-Sce-Qian mapping theorem. We show that, even though the two notions of hyperholomorphic functions are quite different from each other, entire hyperholomorphic functions with exponential bounds play a crucial role in the continuity of infinite order differential operators acting on these two classes of entire hyperholomorphic functions. We point out the remarkable fact that the exponential function of a paravector variable is not in the kernel of the Dirac operator but entire monogenic functions with exponential bounds play an important role in the theory.
