Lower bounds for pseudo-differential operators

N. Lerner; J. Nourrigat

Séminaire Équations aux dérivées partielles (Polytechnique) (1989-1990)

  • page 1-8

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Lerner, N., and Nourrigat, J.. "Lower bounds for pseudo-differential operators." Séminaire Équations aux dérivées partielles (Polytechnique) (1989-1990): 1-8. <http://eudml.org/doc/111989>.

@article{Lerner1989-1990,
author = {Lerner, N., Nourrigat, J.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {lower bound; symbol; Schrödinger operator with magnetic potential},
language = {eng},
pages = {1-8},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Lower bounds for pseudo-differential operators},
url = {http://eudml.org/doc/111989},
year = {1989-1990},
}

TY - JOUR
AU - Lerner, N.
AU - Nourrigat, J.
TI - Lower bounds for pseudo-differential operators
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1989-1990
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 8
LA - eng
KW - lower bound; symbol; Schrödinger operator with magnetic potential
UR - http://eudml.org/doc/111989
ER -

References

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  1. [1] A. Cordoba, C. Fefferman: Wave packets and Fourier integral operators, Comm. P.D.E., 3, 11, 1978, 979-1005. Zbl0389.35046MR507783
  2. [2] C. Fefferman: The uncertainty principle, Bull. AMS, 9, 129-206, 1983. Zbl0526.35080MR707957
  3. [3] C. Fefferman, D.H. Phong: On positivity of pseudo-differential operators Proc. Natl. Ac. Sc. USA75, 4673-4674, 1978. Zbl0391.35062MR507931
  4. [4] C. Fefferman, D.H. Phong: On the lowest eigenvalue of a pseudo-differential operator, Proc. Natl. Ac. Sc. USA76, 6055-6056, 1979. Zbl0434.35071MR554888
  5. [5] C. Fefferman, D.H. Phong: On the asymptotic eigenvalue distribution, Proc. Natl. Ac. Sc. USA77, 5622-5625, 1980. Zbl0443.35082MR589278
  6. [6] C. Fefferman, D.H. Phong: The uncertainty principle and sharp Garding inequalities, CPAM, 34, 285-331, 1981. Zbl0458.35099MR611747
  7. [7] C. Fefferman, D.H. Phong: Symplectic geometry and positivity of pseudodifferential operators, Proc. Natl. Ac. Sc. USA79, 710-713, 1982. Zbl0553.35089MR648064
  8. [8] B. Helffer, J. Nourrigat: Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs, Progress in Math.58, Birkhauser1985. Zbl0568.35003MR897103
  9. [9] I. Herbst: Spectral theory of the operator (p2 + m2)1/2 - ze2/r, Comm. in Math. Phys.53, 285-294, 1977; Errata ibidem55, 316, 1977. Zbl0375.35047MR436854
  10. [10] L. Hörmander: Pseudo-differential operators and non-elliptic boundary problems, Ann. of Math, 83, 129-209, 1966. Zbl0132.07402MR233064
  11. [11] L. Hörmander: The Weyl calculus of pseudo-differential operators, CPAM, 32, 359-443, 1979. Zbl0388.47032MR517939
  12. [12] L. Hörmander: The analysis of linear partial differential operators, four volumes, Berlin, Springer1985. Zbl0601.35001
  13. [13] P.D. Lax, L. Nirenberg: On stability for difference schemes: a sharp form of Garding's inequality, CPAM19, 473-492, 1966. Zbl0185.22801MR206534
  14. [14] A. Melin, Lower bounds for pseudo-differential operators, Ark. Mat.9, 117-140, 1971. Zbl0211.17102MR328393
  15. [15] A. Mohamed, J. Nourrigat: Encadrement du N(λ) pour un opérateur de Schrödinger avec des champs électromagnétiques, to appear J. Math. Pures Appl. Zbl0725.35068
  16. [16] R. Weder: Spectral analysis of pseudo-differential operators, J. Funct. Anal.20, 319-337, 1975. Zbl0317.47035MR402547

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