Analyticity and Supershift with Regular Sampling

Authors

• Fabrizio Colombo, Politecnico di MilanoFollow
• Irene Sabadini, Politecnico di MilanoFollow
• Daniele C. Struppa, Chapman UniversityFollow
• Alain Yger, Université de Bordeaux

Document Type

Article

Publication Date

4-19-2025

Abstract

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.

Comments

This article was originally published in Complex Analysis and its Synergies, volume 11, in 2025. https://doi.org/10.1007/s40627-025-00155-3

Recommended Citation

Colombo, F., Sabadini, I., Struppa, D.C. et al. Analyticity and supershift with regular sampling. Complex Anal Synerg 11, 6 (2025). https://doi.org/10.1007/s40627-025-00155-3

Peer Reviewed

1

Copyright

The authors

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.