Lower bounds for pseudo-differential operators

Nicolas Lerner; Jean Nourrigat

Annales de l'institut Fourier (1990)

  • Volume: 40, Issue: 3, page 657-682
  • ISSN: 0373-0956

Abstract

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This paper contains some new results on lower bounds for pseudo-differential operators whose symbols do not remain positive. Non-negativity of averages of the symbol on canonical images of the unit ball is sufficient to get a Gårding type inequality for Schrödinger operators with magnetic potential and one dimensional pseudo-differential operators.

How to cite

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Lerner, Nicolas, and Nourrigat, Jean. "Lower bounds for pseudo-differential operators." Annales de l'institut Fourier 40.3 (1990): 657-682. <http://eudml.org/doc/74891>.

@article{Lerner1990,
abstract = {This paper contains some new results on lower bounds for pseudo-differential operators whose symbols do not remain positive. Non-negativity of averages of the symbol on canonical images of the unit ball is sufficient to get a Gårding type inequality for Schrödinger operators with magnetic potential and one dimensional pseudo-differential operators.},
author = {Lerner, Nicolas, Nourrigat, Jean},
journal = {Annales de l'institut Fourier},
keywords = {nonpositive symbol; Gårding’s inequality; lower bounds; magnetic potential},
language = {eng},
number = {3},
pages = {657-682},
publisher = {Association des Annales de l'Institut Fourier},
title = {Lower bounds for pseudo-differential operators},
url = {http://eudml.org/doc/74891},
volume = {40},
year = {1990},
}

TY - JOUR
AU - Lerner, Nicolas
AU - Nourrigat, Jean
TI - Lower bounds for pseudo-differential operators
JO - Annales de l'institut Fourier
PY - 1990
PB - Association des Annales de l'Institut Fourier
VL - 40
IS - 3
SP - 657
EP - 682
AB - This paper contains some new results on lower bounds for pseudo-differential operators whose symbols do not remain positive. Non-negativity of averages of the symbol on canonical images of the unit ball is sufficient to get a Gårding type inequality for Schrödinger operators with magnetic potential and one dimensional pseudo-differential operators.
LA - eng
KW - nonpositive symbol; Gårding’s inequality; lower bounds; magnetic potential
UR - http://eudml.org/doc/74891
ER -

References

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  1. [1] A. CORDOBA, C. FEFFERMAN, Wave packets and Fourier integral operators, Comm. PDE, 3, 11 (1978), 979-1005. Zbl0389.35046MR80a:35117
  2. [2] C.L. FEFFERMAN, The uncertainty principle, Bull. AMS, 9 (1983), 129-206. Zbl0526.35080MR85f:35001
  3. [3] C. FEFFERMAN, D.H. PHONG, On positivity of pseudo-differential operators, Proc. Natl. Ac. Sc. USA, 75 (1978), 4673-4674. Zbl0391.35062MR80b:47064
  4. [4] C. FEFFERMAN, D.H. PHONG, On the lowest eigenvalue of a pseudo-differential operator, Proc. Natl. Ac. Sc. USA, 76 (1979), 6055-6056. Zbl0434.35071MR81d:47032
  5. [5] C. FEFFERMAN, D.H. PHONG, On the asymptotic eigenvalue distribution, Proc. Natl. Ac. Sc. USA, 77 (1980), 5622-5625. Zbl0443.35082MR82h:35101
  6. [6] C. FEFFERMAN, D.H. PHONG, The uncertainty principle and sharp Garding inequalities, CPAM, 34 (1981), 285-331. Zbl0458.35099MR82j:35140
  7. [7] C. FEFFERMAN, D.H. PHONG, Symplectic geometry and positivity of pseudo-differential operators, Proc. Natl. Ac. Sc. USA, 79 (1982), 710-713. Zbl0553.35089MR83f:35108
  8. [8] B. HELFFER, J. NOURRIGAT, Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs, Progress in Math. 58, Birkhauser, 1985. Zbl0568.35003MR88i:35029
  9. [9] L. HÖRMANDER, Pseudo-differential operators and non-elliptic boundary problems, Ann. of Math., 83 (1966), 129-209. Zbl0132.07402MR38 #1387
  10. [10] L. HÖRMANDER, The Weyl calculus of pseudo-differential operators, CPAM, 32 (1979), 359-443. Zbl0388.47032
  11. [11] L. HÖRMANDER, The analysis of linear partial differential operators, four volumes, Berlin, Springer, 1985. Zbl0601.35001
  12. [12] P.D. LAX, L. NIRENBERG, On stability for difference schemes : a sharp form of Garding's inequality, CPAM 19 (1966), 473-492. Zbl0185.22801MR34 #6352
  13. [13] 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
  14. [14] J. NOURRIGAT, Subelliptic systems, to appear in Comm. PDE. Zbl0723.35089

Citations in EuDML Documents

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  1. Ronan Pouliquen, Lower bounds for Schrödinger operators in H¹(ℝ)
  2. Jean-Michel Bony, Sommes de carrés de fonctions dérivables
  3. Frédéric Hérau, Fefferman's SAK principle in one dimension
  4. Jean-Michel Bony, Décomposition des fonctions positives en sommes de carrés
  5. Nicolas Lerner, Opérateurs pseudo-différentiels et capacités symplectiques
  6. Bernard Helffer, Remarks on decay of correlations and Witten laplacians III. Application to logarithmic Sobolev inequalities

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