2024/12/22 by Colombo, F., Fabrizia Mantovani, Stefano Pinton +4 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2412.16999
openalex publication_date 2024/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Superoscillatory functions represent a counterintuitive phenomenon in physics but also in mathematics, where a band-limited function oscillates faster than its highest Fourier component. They appear in various contexts, including quantum mechanics, as a result of a weak measurement introduced by Y. Aharonov and collaborators. These functions can be extended to the complex variable and are a specific instance of the more general notion of supershift. The aim of this paper is to extend the notion of superoscillatory functions to the hypercomplex setting. This extension is richer than the complex case since the Fueter-Sce extension theorem for Clifford-valued functions provides two notions of hyperholomorphic functions. We will explore these notions and address the corresponding superoscillating theories.