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) 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.

Superoscillating Sequences Towards Approximation in S or S′ -Type Spaces and Extrapolation

Colombo F.;
2019-01-01

Abstract

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) 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.
2019
Approximation by superoscillations; Band-limited signals; Schwartz space; Tempered distributions
File in questo prodotto:
File Dimensione Formato  
11311-1126678_Colombo F..pdf

accesso aperto

: Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione 833.86 kB
Formato Adobe PDF
833.86 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1126678
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 15
  • ???jsp.display-item.citation.isi??? 12
social impact