Evolution of Superoscillations in the Klein-Gordon Field

Y. Aharonov, F. Colombo*, I. Sabadini, D. C. Struppa, J. Tollaksen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

Superoscillating functions are band-limited functions that can oscillatefaster than their fastest Fourier component. There is nowadays a large literatureon the evolution of superoscillations under Schrödinger equation with differenttype of potentials. In this paper, we study the evolution of superoscillations underthe Klein-Gordon equation and we describe in precise mathematical terms in whatsense superoscillations persist in time during the evolution. The main tools forour investigation are convolution operators acting on spaces of entire functionsand Green functions.

Original languageEnglish
Pages (from-to)171-189
Number of pages19
JournalMilan Journal of Mathematics
Volume88
Issue number1
DOIs
StatePublished - 1 Jun 2020
Externally publishedYes

Keywords

  • Klein-Gordon equation
  • Superoscillating functions
  • convolution operators
  • entire functions with growth conditions

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