Abstract
We investigate the discrete Fuglede conjecture and the Pompeiu problem on finite abelian groups and develop a strong connection between the two problems. We give a geometric condition under which a multiset of a finite abelian group has the discrete Pompeiu property. Using this description and the revealed connection we prove that Fuglede’s conjecture holds for , where and are different primes. In particular, we show that every spectral subset of tiles the group. Further, using our combinatorial methods we give a simple proof for the statement that Fuglede’s conjecture holds for .
Citation
Gergely Kiss. Romanos Diogenes Malikiosis. Gábor Somlai. Máté Vizer. "On the discrete Fuglede and Pompeiu problems." Anal. PDE 13 (3) 765 - 788, 2020. https://doi.org/10.2140/apde.2020.13.765
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