2023/10/17 by Fabrizio Colombo, Colombo, F., Irene Sabadini +5 · 1 citation
Computer Science · Mathematics · #Complex Variables (math.CV) #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.2310.11528
openalex publication_date 2023/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notion of supershift (in itself a generalization of the notion of superoscillation arising in quantum mechanics) expresses the fact that the sampling of a function in an interval allows to compute the values of the function far from the interval. In this paper we study the relation between supershift and real analyticity. We use a classical result due to Serge Bernstein to show that real analyticity for a complex valued function implies a strong form of supershift. On the other hand, we use a parametric version of a result by Leonid Kantorovitch to show that the converse is not true. We additionally study the stability of functions that satisfy suitable supershift requirements under multiplication by complex numbers or primitivization.