Article (Scientific journals)
The discrete Pompeiu problem on the plane
Kiss, Gergely; Laczkovich, Miklós; Vincze, Csaba
2018In Monatshefte für Mathematik
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Keywords :
39B32 (primary); 30D05 (primary); 43A45 (secondary)
Abstract :
[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.
Disciplines :
Mathematics
Author, co-author :
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
External co-authors :
no
Language :
English
Title :
The discrete Pompeiu problem on the plane
Publication date :
June 2018
Journal title :
Monatshefte für Mathematik
ISSN :
1436-5081
Publisher :
Springer, Vienna, Austria
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 21 November 2017

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