The General Theory of Superoscillations and Supershifts in Several Variables

Authors

Fabrizio Colombo, Politecnico di MilanoFollow
Stefano Pinton, Politecnico di MilanoFollow
Irene Sabadini, Politecnico di MilanoFollow
Daniele C. Struppa, Chapman UniversityFollow

Document Type

Article

Publication Date

10-17-2023

Abstract

In this paper we describe a general method to generate superoscillatory functions of several variables starting from a superoscillating sequence of one variable. Our results are based on the study of suitable infinite order differential operators acting on holomorphic functions with growth conditions of exponential type. Additional constraints are required when dealing with infinite order differential operators whose symbol is a function that is holomorphic in some open set, but not necessarily entire. The results proved for superoscillating sequences in several variables are extended to sequences of supershifts in several variables.

Comments

This article was originally published in Journal of Fourier Analysis and Applications, volume 29, in 2023. https://doi.org/10.1007/s00041-023-10048-w

Recommended Citation

Colombo, F., Pinton, S., Sabadini, I. et al. The General Theory of Superoscillations and Supershifts in Several Variables. J Fourier Anal Appl 29, 66 (2023). https://doi.org/10.1007/s00041-023-10048-w

Peer Reviewed

1

Creative Commons License

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