• Corpus ID: 118065990

On the One-Dimentional Pompeiu Problem

@article{Barutello2011OnTO,
  title={On the One-Dimentional Pompeiu Problem},
  author={Vivina L. Barutello and Camillo Costantini},
  journal={arXiv: Classical Analysis and ODEs},
  year={2011}
}
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… 

Figures from this paper

References

SHOWING 1-8 OF 8 REFERENCES

A note on the Pompeiu problem for convex domains

As the Pompeiu problem named after the late Rumanian mathematician Dimitric Pompeiu we shall denote the following question. Let S denote the group of all rigid motions of the plane. Given a bounded

A note on a problem of D. Pompeiu

for some subset T~ c T. Does this imply tha t f (x , y ) 0 ? POMPEIU thought that if B is a disc and if T1 = T, thenf (x , y) 0 [6]. I t was noted later that the result is not correct in this form.

Spectral synthesis and the Pompeiu problem

© Annales de l’institut Fourier, 1973, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions

A Bibliographic Survey of the Pompeiu Problem

A compact set K ⊂ ℝ n is said to have the Pompeiu property (PP) if the only function \( % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm %

Sur une proprit de functions continue dpendent de plusieur variables

  • Bull. Sci. Math.,
  • 1929

Sur certain systmes d’quationslinaires et sur une proprit intgrale de functions de plusieur variables

  • C. R. Acam. Sci. Paris,
  • 1929

Sur une proprit intgrale de functions de deux variables relles

  • Bull. Sci. Acad. Royale Belgique,
  • 1929