2023/11/04 by Fabrizio Colombo, Rolf Soeren Krausshar, Colombo, F. +5
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Waves and Solitons #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2311.02381
openalex publication_date 2023/11/04 · openalex created_date 2023/11/08 · openalex updated_date 2026/07/28
Infinite order differential operators appear in different fields of mathematics and physics. In the past decade they turned out to play a crucial role in the theory of superoscillations and provided new insight in the study of the evolution as initial data for the Schrödinger equation. Inspired by the infinite order differential 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. Precisely, we consider homomorphisms acting on functions in the kernel of the Dirac operator. For this class of functions, often called monogenic functions, we introduce the proximate order and prove some fundamental properties. As important application we are able to characterize infinite order differential operators that act continuously on spaces of monogenic entire functions.