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The discrete Pompeiu problem on the plane Kiss, Gergely ; ; in Monatshefte für Mathematik (2018) 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 100 (5 UL)A characterisation of associative idempotent nondecreasing functions with neutral elements Kiss, Gergely ; ; Marichal, Jean-Luc et al Scientific Conference (2016, June) Detailed reference viewed: 80 (14 UL)Linear functional equations, differential operators and spectral synthesis. Kiss, Gergely ; in Aequationes Mathematicae (2015), 89(2), 301328 Detailed reference viewed: 101 (11 UL)Decomposition of balls into finitely many pieces Kiss, Gergely ; in Mathematika (2011), 57(1), 89-107 Detailed reference viewed: 55 (4 UL) |
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