Efficient method to create superoscillations with generic target behavior

Abstract

We introduce a new numerically stable method for constructing superoscillatory wave forms in an arbitrary number of dimensions. The method allows the construction of superoscillatory square-integrable functions that match any desired smooth behavior in their superoscillatory region to arbitrary accuracy.

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Acknowledgements

AK and BŠ acknowledge useful discussions with Lucien Hardy. AK is supported by a Discovery Grant of the Natural Sciences and Engineering Research Council of Canada (NSERC) and by a Google Faculty Research Award. BŠ is supported in part by the Perimeter Institute, which is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Economic Development, Job Creation and Trade.

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Correspondence to Barbara Šoda.

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Šoda, B., Kempf, A. Efficient method to create superoscillations with generic target behavior. Quantum Stud.: Math. Found. 7, 347–353 (2020). https://doi.org/10.1007/s40509-020-00226-6

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Keywords

  • Superoscillations
  • Superresolution
  • Fourier