Skip to main content
SpringerLink
Log in

Le probleme de Pompeiu local

  • Published:
Journal d’Analyse Mathématique Aims and scope

Abstract

A sufficient condition is given so that in a ballB(x, R), there are no functions whose average over all Euclidean motions of an open bounded set Ω which are contained inB(x, R) vanish, except for the zero function.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Bibliographie

  1. C. A. Berenstein and R. Gay,A local version of the two-circles theorem, Isr. J. Math.55 (1986), 267–288.

    Article  MATH  MathSciNet  Google Scholar 

  2. C. A. Berenstein and L. Zalcman,Pompeiu's problem on symmetric spaces, Comment. Math. Helv.55 (1980), 593–621.

    Article  MATH  MathSciNet  Google Scholar 

  3. L. Brown, B. M. Schreiber and B. A. Taylor,Spectral synthesis and the Pompeiu problem, Ann. Inst. Fourier23 (1973), 125–154.

    MathSciNet  Google Scholar 

  4. A. M. Cormack and E. Quinto, A Radon transform through the origin in {ie165-1} and applications to the classical Darboux equation, Trans. Am. Math. Soc.260 (1980), 575–581.

    Article  MATH  MathSciNet  Google Scholar 

  5. S. Helgason,Groups and Geometric Analysis, Academic Press, New York, 1984.

    MATH  Google Scholar 

  6. L. Hörmander,The Analysis of Linear Partial Differential Operators, Vols. I and II, Springer-Verlag, Berlin, 1983.

    Google Scholar 

  7. N. N. Lebedev,Special Functions and their Applications, Dover Publications, Inc., New York, 1972.

    MATH  Google Scholar 

  8. B. Ja. Levin,Distribution of Zeros of Entire Functions, Am. Math. Soc., 1964.

  9. L. Zalcman,Analyticity and the Pompeiu problem, Arch. Rat. Mech. Anal.47 (1972).

Download references

Author information

Authors and Affiliations

  1. Mathematics Department and Systems Research Center, University of Maryland, 20742, College Park, MD, USA

    Carlos A. Berenstein

  2. U.E.R. de Mathématiques et d'Informatique, Université de Bordeaux I, Unité Associée au C.N.R.S. no. 226 351, cours de la Libération, 33406, Talence, Cedex, France

    Roger Gay

Authors
  1. Carlos A. Berenstein
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roger Gay
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

La recherche de C. A. Berenstein a été effectuée dans le cadre des constrats NSF-DMS 8703072 et ARO-DAA L 0386K0115. M. Berenstein remercie ces organismes pour leur appui.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Berenstein, C.A., Gay, R. Le probleme de Pompeiu local. J. Anal. Math. 52, 133–166 (1981). https://doi.org/10.1007/BF02820476

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02820476

Search

Navigation