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 mailto [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 ORBilu)
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

File(s) associated to this reference

Fulltext file(s):

FileCommentaryVersionSizeAccess
Open access
pompeiu.pdfPublisher postprint375.85 kBView/Open

Bookmark and Share SFX Query

All documents in ORBilu are protected by a user license.