Superoscillating Sequences Towards Approximation in S or S′ -Type Spaces and Extrapolation
Aharonov–Berry superoscillations are band-limited sequences of functions that happen to oscillate asymptotically faster than their fastest Fourier component. In this paper we analyze in what sense functions in the Schwartz space S(R,C)" role="presentation">S(R,C) or in some of its subspaces, tempered distributions or also ultra-distributions, could be approximated over compact sets or relatively compact open sets (depending on the context) by such superoscillating sequences. We also show how one can profit of the existence of such sequences in order to extrapolate band-limited signals with finite energy from a given segment of the real line.
Colombo, F., Struppa, D.C. & Yger, A. Superoscillating Sequences Towards Approximation in S or S′-Type Spaces and Extrapolation. J Fourier Anal Appl 25, 242–266 (2019). https://doi.org/10.1007/s00041-018-9592-8