Entire Monogenic Functions of Given Proximate Order and Continuous Homomorphisms

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 t...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2024-02, Vol.21 (2), Article 44
Main Authors: Colombo, Fabrizio, Krausshar, Rolf Soeren, Pinton, Stefano, Sabadini, Irene
Format: Article
Language:English
Subjects:
Differential equations
Entire functions
Homomorphisms
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators (mathematics)
Quantum mechanics
Schrodinger equation
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Summary: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 an important application, we are able to characterize infinite order differential operators that act continuously on spaces of monogenic entire functions.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-023-02585-x