Skip to main content
Log in

Reconstruction from local averages involving discrete measures

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Abstract

The aim of the paper is to solve the convolution equation of the type f ⋆ µ =g, where g is a given function and µ is the given finitely supported measure. A solution is constructed for the above said convolution equation.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Delsarte, J: Les fonctions moyenne-periodiques, J.Math. Pures Appl., 14 (1935), 403–453

    MATH  Google Scholar 

  2. Devaraj, P, Rana, I.K.: Vector valued mean-periodic functions, J. Aust. Math. Soc., 72 (2002), 363–388

    Article  MATH  MathSciNet  Google Scholar 

  3. Edgar, G.A., Rosenblatt, J.M.: Difference equations over locally compact abelain groups, Trans. Amer. Math. Soc., 253 (1979), 273–289

    MATH  MathSciNet  Google Scholar 

  4. Ehrenpreis, L.: Solutions of some problems of division III, Amer. J. Math., 78 (1956), 685–715

    Article  MATH  MathSciNet  Google Scholar 

  5. John, F.: Continuous dependence on data for solutions of partial differential equations with prescribed bound, Comm. Pure Appl. Math., 13 (1960), 551–585

    Article  MATH  MathSciNet  Google Scholar 

  6. Hörmander L.: On the range of convolution operators, Ann. Math., 76 (1968), 148–169

    Article  Google Scholar 

  7. Malgrange, B.: Existence et approximation des solutions des equations aux derivees partielles et des equations de convolutions, Ann. Inst. Fourier Grenoble, 6 (1955–56), 271–355

    MathSciNet  Google Scholar 

  8. Novak, E, Rana, I.K.: On the unsmoothing of functions on the real line, Proc. Nede. Acad.Sci., Ser. A 89 (1986), 201–207

    MathSciNet  Google Scholar 

  9. Rana, I.K.: Unsmoothing over balls via plane wave decomposition, Rend. Cir. Mat. Palermo, 34 (1990), 217–234

    Article  MathSciNet  Google Scholar 

  10. Schwartz, L.: Theorie generale des fonctions moyenne-periodiquies, Ann. Math., 48 (1947), 857–929

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to P. Devaraj.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Devaraj, P. Reconstruction from local averages involving discrete measures. Rend. Circ. Mat. Palermo 59, 261–266 (2010). https://doi.org/10.1007/s12215-010-0019-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12215-010-0019-x

Keywords

Mathematics Subject Classification (2000)

Navigation