Reference : The discrete Pompeiu problem on the plane |

Scientific journals : Article | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/33082 | |||

The discrete Pompeiu problem on the plane | |

English | |

Kiss, Gergely [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |

Laczkovich, Miklós [Eötvös Loránd University Budapest > Analysis] | |

Vincze, Csaba [University of Debrecen] | |

Jun-2018 | |

Monatshefte für Mathematik | |

Springer | |

Yes (verified by ORBi^{lu}) | |

0026-9255 | |

1436-5081 | |

Vienna | |

Austria | |

[en] 39B32 (primary) ; 30D05 (primary) ; 43A45 (secondary) | |

[en] We say that a finite subset $E$ of the Euclidean plane $\R^2$ has
the discrete Pompeiu property with respect to isometries (similarities), if, whenever $f:\R^2\to \C$ is such that the sum of the values of $f$ on any congruent (similar) copy of $E$ is zero, then $f$ is identically zero. We show that every parallelogram and every quadrangle with rational coordinates has the discrete Pompeiu property with respect to isometries. We also present a family of quadrangles depending on a continuous parameter having the same property. We investigate the weighted version of the discrete Pompeiu property as well, and show that every finite linear set with commensurable distances has the weighted discrete Pompeiu property with respect to isometries, and every finite set has the weighted discrete Pompeiu property with respect to similarities. | |

http://hdl.handle.net/10993/33082 |

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