Gergely Kiss: The discrete Pompeiu problem on Euclidean spaces

Let K be a nonempty finite subset of the Euclidean space R^k (k ≥ 2). In this talk we discuss the solution of the following so-called discrete Pompeiu problem: Is it true that whenever a function f : R^k → C is such that the sum of f on every congruent copy of K is zero, then f vanishes everywhere? Some important consequences of the result will also be presented such as every finite subset of R^k having at least two elements is a Jackson set.
This is a joint work with Miklós Laczkovich.