Reference : The discrete Pompeiu problem on the plane
Scientific Presentations in Universities or Research Centers : Scientific presentation in universities or research centers
Physical, chemical, mathematical & earth Sciences : Mathematics
The discrete Pompeiu problem on the plane
Kiss, Gergely mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
DCG-DISOPT seminar
from 26-11-2017 to 01-12-20017
[en] The discrete Pompeiu problem is stemmed from an integral-geometric question on the plane. The problem is whether we can reconstruct a function if we know the average values of the function on every congruent copy of a given pattern. After introducing the theory of spectral analysis on discrete Abelian groups, I show some results for the discrete version of the problem. One of the arguments is connected to a coloring problem of the plane. One of them is a geometric construction and some others based on some geometric and combinatoric properties of the plane. I also mention some unsolved questions of the topic. My talk is based on a joint work with M. Laczkovich and Cs. Vincze.

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