Coercive inequalities for Pseudodifferential operators of constant rank

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

  • 33 Accesses


Operators are studied whose symbol satisfies a condition of constant rank and a priori estimates developed which hold essentially on the complement of an approximate null space of the operator. A limit absorption result is then established using a technique first described by Agmon.


  1. [1]

    S. Agmon,Spectral properties of Schrödinger operators, Actes Congrès intern. Math., tome 2, Gauthier-Villars, Paris (1971), pp. 679–683.

  2. [2]

    M. Atiyah -R. Bott,A Lefschetz fixed point formula for elliptic complexes I, Ann. of Math.,86 (1967), pp. 374–607.

  3. [3]

    G. de Rham,Variétés differentiables, formes, courants, formes harmonique, Act. Sci. et Ind., vol.122, Hermann, Paris (1955).

  4. [4]

    J. J. Duierstermatt -L. Hörmander,Fourier integral operators II, Acta Math.,128 (1972), pp. 183–269.

  5. [5]

    D. M. Eidus,The principle of limit amplitude, Russian Math. Surveys,24 (1969), pp. 97–167.

  6. [6]

    C. Goldstein,Perturbation of non selfajdoint operators, I, Arch. Rat. Mech. Anal.,37 (1970), pp. 268–296.

  7. [7]

    L. Hörmander,Pseudo-differential operators and non-elliptic boundary value problems, Ann. Math.,83 (1966), pp. 129–209.

  8. [8]

    L. Hörmander,Fourier integral operators I, Acta Math.,127 (1971), pp. 80–182.

  9. [9]

    L. Hörmander,Pseudo-differential operators and hypoelliptic equations, Amer. Math. Soc. Symp. Pure Math.,10 (1966);Singular integral operators, pp. 138–183.

  10. [10]

    S. T. Kuroda,Scattering for differential operators - I:Operator theory, J. Math. Soc. Japan,25 (1973), pp. 75–104.

  11. [11]

    S. T. Kuroda,Scattering theory for differential operators - II:Self adjoint elliptic operators, J. Math. Soc. Japan,25 (1973), pp. 222–234.

  12. [12]

    J. A. La Vita - B. Wendroff,A coerciveness inequality for some non-elliptic differential operators, Report of Dept. of Math., University of Denver (1970).

  13. [13]

    C. P. Putnam,Commutation properties of Hilbert space operators and related topics, Ergebnisse der Mathematik, Band 35, Springer-Verlag, Berlin (1967).

  14. [14]

    J. V. Ralston,Conservative first order hyperbolic systems, Trans. Amer. Math. Soc.,194 (1974), pp. 27–51.

  15. [15]

    F. Riesz -B. St. Nagy,Functional Analysis, Ungar, New York (1955).

  16. [16]

    L. Sarason,Remarks on an inequality of Schulenberger and Wilcox, Ann. Mat. Pura Appl.,92 (1972), pp. 23–28.

  17. [17]

    J. R. Schulenberger -C. H. Wilcox,Coerciveness inequalities for nonelliptic systems of partial differential equations, Ann. Mat. Pura Appl.,88 (1971), pp. 229–306.

  18. [18]

    L. Schwartz,Theorie des distributions I, II, Act. Sci. et Ind., vols. 1245, 1122, Hermann, Paris (1957, 1951).

  19. [19]

    M. Thompson,Scattering for perturbations of uniformly propagative symmetric hyperbolic systems, Proc. Lond. Math. Soc.,30 (1975), pp. 405–429.

  20. [20]

    M. Thompson,The spectral theory of perturbed hypoelliptic operators, to appear in Proc. Lond. Math. Soc.,34 (1977), pp. 421–437.

  21. [21]

    C. H. Wilcox,Wave operators and asymptotic solutions of wave propagation problems of classical physics, Arch. Rat. Mech. Anal.,22 (1966), pp. 37–78.

  22. [22]

    K. Yajima,The limit absorption principle for uniformly propagative systems, J. Far. Sci., Tokyo University, Sec. 1-A,21 (1974), pp. 119–131.

  23. [23]

    N. Yamada,On the principle of limit absorption for the Dirac operator, Publ. KIMS, Kyoto University,8 (1972–73), pp. 576–606.

Download references

Author information

Additional information

Entrata in Redazione il 1è ottobre 1975.

Research supported by the Science Research Council under contract B/SR/97915.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Thompson, M. Coercive inequalities for Pseudodifferential operators of constant rank. Annali di Matematica 115, 1–15 (1977).

Download citation


  • Null Space
  • Pseudodifferential Operator
  • Limit Absorption
  • Absorption Result
  • Constant Rank