Skip to main content
SpringerLink
Log in

Lower bounds for systems with double characteristics

  • Published:
Journal d’Analyse Mathématique Aims and scope

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

References

  1. L.Boutet de Monvel,Hypoelliptic operators with double characteristics and related pseudo-differential operators, Comm. Pure Appl. Math.27 (1974), 585–639.

    Article  MATH  MathSciNet  Google Scholar 

  2. L.Boutet de Monvel and P. Trèves,On a class of systems of pseudodifferential equations with double characteristics, Comm. Pure Appl. Math.27 (1974), 59–89.

    Article  MATH  MathSciNet  Google Scholar 

  3. L.Boutet de Monvel, A. Grigis and B. Helffer,Paramétrixes d’opérateurs pseudo-différentiels à caractéristiques multiples, Astérisque34-35 (1976), 93–121.

    Google Scholar 

  4. R. Brummelhuis,Sur les inégalités de Gårding pour les systèmes d’opérateurs pseudo-différentiels, C. R. Acad. Sri.Paris315, Serie I (1992), 149–152.

    MATH  MathSciNet  Google Scholar 

  5. R.Brummelhuis,A Melin inequality for systems of pseudodifferential operators, Preprint (1997).

  6. B. Helffer,Invariants associés à une classe d’opérateurs pseudodifférentiels et applications à l’hypoellipticité, Ann. Inst. Fourier26 (1976), 55–70.

    MATH  MathSciNet  Google Scholar 

  7. L. Hörmander,The Cauchy problem for differential equations with double characteristics, J. Analyse Math.32 (1977), 118–196.

    Article  MATH  MathSciNet  Google Scholar 

  8. L. Hörmander,On the subelliptic test estimates, Comm. Pure Appl. Math.33 (1980), 339–363.

    Article  MATH  MathSciNet  Google Scholar 

  9. L. Hörmander,The Analysis of Linear Partial Differential Operators, Vols. I-IV, Springer-Verlag, 1983/85.

  10. P.D. Lax and L. Nirenberg,On stability of difference schemes: a sharp form of Gårding’s inequality, Comm. Pure Appl. Math.19 (1966), 473–492.

    Article  MATH  MathSciNet  Google Scholar 

  11. F. Maruyama,Questions de théorie spectrale pour des opérateurs différentiels et pseudo-différentiels, Thèse, Université de Paris Nord, 1997.

  12. A. Melin,Lower bounds for pseudo-differential fnoperators, Ark. Mat.9 (1971), 117–140.

    Article  MATH  MathSciNet  Google Scholar 

  13. A. Mohamed,Etude spectrale d’opérateurs hypoelliptiques à caractéristiques multiples, II, Comm. Partial Differential Equations8 (1983), 247–316.

    Article  MATH  MathSciNet  Google Scholar 

  14. C. Parenti and A. Parmeggiani,Some remarks on almost-positivity of ψdo’s, Boll. Un. Mat. Ital. B (8)1-B (1998), 187–215.

    MathSciNet  Google Scholar 

  15. C. Parenti and A. Parmeggiani,A generalization of Hörmander’s inequality-I, Comm. Partial Differential Equation25 (2000), 457–506.

    Article  MATH  MathSciNet  Google Scholar 

  16. A.Parmeggiani and M. Wakayama,Non-commutative harmonic oscillators-I, Forum Math., to appear.

  17. A.Parmeggiani and M. Wakayama,Non-commutative harmonic oscillators-II, Forum Math., to appear.

  18. A. Parmeggiani and M. Wakayama,Oscillator representations and systems of ordinary differential equations, Proc. Nat. Acad. Sci. U.S.A.98 (2001), 26–30.

    Article  MATH  MathSciNet  Google Scholar 

  19. P.R. Popivanov,On the Hypoellipticity of a Pseudo-differential System With a Diagonal Principal Symbol, Partial Differential Equations, Banach Center Publications Vol. 10, 1983, pp. 279–299.

    MathSciNet  Google Scholar 

  20. M. Shubin,Pseudodifferential Operators and Spectral Theory, Springer-Verlag, Berlin, 1987.

    MATH  Google Scholar 

  21. J. Sjöstrand,Parametrices for pseudodifferential operators with multiple characteristics, Ark. Mat.12 (1974), 85–130.

    Article  MATH  MathSciNet  Google Scholar 

  22. L.-Y. Sung,Positivity of a system of differential operators, J. Differential Equations66 (1987), 71–89.

    Article  MATH  MathSciNet  Google Scholar 

  23. M. Taylor,Reflection of singularities of solutions to systems of differential equations, Comm. Pure Appl. Math.28 (1975), 457–478.

    Article  MATH  MathSciNet  Google Scholar 

  24. M. Taylor,Pseudodifferential Operators, Princeton University Press, 1981.

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Bologna, Piazza di Porta S. Donato 5, 40127, Bologna, Italy

    Cesare Parenti

  2. Department of Mathematics, University of Bologna, Piazza di Porta S. Donato 5, 40127, Bologna, Italy

    Alberto Parmeggiani

Authors
  1. Cesare Parenti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alberto Parmeggiani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cesare Parenti.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Parenti, C., Parmeggiani, A. Lower bounds for systems with double characteristics. J. Anal. Math. 86, 49–91 (2002). https://doi.org/10.1007/BF02786644

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02786644

Keywords

Search

Navigation