• Corpus ID: 118065990

On the One-Dimentional Pompeiu Problem

  title={On the One-Dimentional Pompeiu Problem},
  author={Vivina L. Barutello and Camillo Costantini},
  journal={arXiv: Classical Analysis and ODEs},
We investigate the Pompeiu property for subsets of the real line, under no assumption of connectedness. In particular we focus our study on finite unions of bounded (disjoint) intervals, and we emphasize the different results corresponding to the cases where the function in question is supposed to have constant integral on all isometric images, or just on all the translation-images of the domain. While no set of the previous kind enjoys the Pompeiu property in the latter sense, we provide a… 

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