×

zbMATH — the first resource for mathematics

Lower bounds for pseudo-differential operators. (English) Zbl 0703.35182
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.
Reviewer: N.Lerner

MSC:
35S05 Pseudodifferential operators as generalizations of partial differential operators
35J10 Schrödinger operator, Schrödinger equation
35P15 Estimates of eigenvalues in context of PDEs
PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML
References:
[1] A. CORDOBA, C. FEFFERMAN, Wave packets and Fourier integral operators, Comm. PDE, 3, 11 (1978), 979-1005. · Zbl 0389.35046
[2] C.L. FEFFERMAN, The uncertainty principle, Bull. AMS, 9 (1983), 129-206. · Zbl 0526.35080
[3] C. FEFFERMAN, D.H. PHONG, On positivity of pseudo-differential operators, Proc. Natl. Ac. Sc. USA, 75 (1978), 4673-4674. · Zbl 0391.35062
[4] C. FEFFERMAN, D.H. PHONG, On the lowest eigenvalue of a pseudo-differential operator, Proc. Natl. Ac. Sc. USA, 76 (1979), 6055-6056. · Zbl 0434.35071
[5] C. FEFFERMAN, D.H. PHONG, On the asymptotic eigenvalue distribution, Proc. Natl. Ac. Sc. USA, 77 (1980), 5622-5625. · Zbl 0443.35082
[6] C. FEFFERMAN, D.H. PHONG, The uncertainty principle and sharp garding inequalities, CPAM, 34 (1981), 285-331. · Zbl 0458.35099
[7] C. FEFFERMAN, D.H. PHONG, Symplectic geometry and positivity of pseudo-differential operators, Proc. Natl. Ac. Sc. USA, 79 (1982), 710-713. · Zbl 0553.35089
[8] B. HELFFER, J. NOURRIGAT, Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs, Progress in Math. 58, Birkhauser, 1985. · Zbl 0568.35003
[9] L. HÖRMANDER, Pseudo-differential operators and non-elliptic boundary problems, Ann. of Math., 83 (1966), 129-209. · Zbl 0132.07402
[10] L. HÖRMANDER, The Weyl calculus of pseudo-differential operators, CPAM, 32 (1979), 359-443. · Zbl 0388.47032
[11] L. HÖRMANDER, The analysis of linear partial differential operators, four volumes, Berlin, Springer, 1985. · Zbl 0601.35001
[12] P.D. LAX, L. NIRENBERG, On stability for difference schemes : a sharp form of Garding’s inequality, CPAM 19 (1966), 473-492. · Zbl 0185.22801
[13] A. MOHAMED, J. NOURRIGAT, Encadrement du N(λ) pour un opérateur de Schrödinger avec des champs électromagnétiques, to appear J. Math. Pures Appl. · Zbl 0725.35068
[14] J. NOURRIGAT, Subelliptic systems, to appear in Comm. PDE. · Zbl 0723.35089
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.