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Evolution of Superoscillations in the Klein-Gordon Field

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Abstract

Superoscillating functions are band-limited functions that can oscillate faster than their fastest Fourier component. There is nowadays a large literature on the evolution of superoscillations under Schrödinger equation with different type of potentials. In this paper, we study the evolution of superoscillations under the Klein-Gordon equation and we describe in precise mathematical terms in what sense superoscillations persist in time during the evolution. The main tools for our investigation are convolution operators acting on spaces of entire functions and Green functions.

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Authors and Affiliations

  1. Schmid College of Science and Technology, Chapman University, Orange, 92866, CA, USA

    Y. Aharonov & J. Tollaksen

  2. Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi, 9, 20133, Milano, Italy

    F. Colombo & I. Sabadini

  3. The Donald Bren Presidential Chair in Mathematics, Chapman University, Orange, USA

    D. C. Struppa

Authors
  1. Y. Aharonov
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  2. F. Colombo
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  3. I. Sabadini
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  4. D. C. Struppa
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  5. J. Tollaksen
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Corresponding author

Correspondence to F. Colombo.

Additional information

Seminario Matematico e Fisico Lecture by Yakir Aharonov: June 18, 2019

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Aharonov, Y., Colombo, F., Sabadini, I. et al. Evolution of Superoscillations in the Klein-Gordon Field. Milan J. Math. 88, 171–189 (2020). https://doi.org/10.1007/s00032-020-00310-x

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  • DOI: https://doi.org/10.1007/s00032-020-00310-x

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