Year: 2025
Type: article
Abstract: 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.
Source: Journal of Geometric Analysis
Authors: F. Colombo, F. Mantovani, S. Pinton, P. Schlosser
Institutions: Politecnico di Milano, Graz University of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4409306065