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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 ) or in some of its subspaces, tempered distributions or also...
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Published in: | The Journal of fourier analysis and applications 2019-02, Vol.25 (1), p.242-266 |
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Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | 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. |
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ISSN: | 1069-5869 1531-5851 |
DOI: | 10.1007/s00041-018-9592-8 |