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A necessary and sufficient condition for a lower bound for fourth-order pseudodifferential operators

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Journal d’Analyse Mathématique Aims and scope

An Erratum to this article was published on 01 December 1997

Abstract

We give necessary and sufficient conditions for the lower bound {fx55-01} to hold for any compact setK ⊂X, an open set ofR n, andP =P* ∃ ψ 4 phg (X) with p(x, ξ) ~ q 22 + p3 + p2 + ..., q2 beingtransversally elliptic with respect to the characteristic manifold Σ =q 2 -1 (0).

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References

  1. C. L. Fefferman,The uncertainty principle, Bull. Amer. Math. Soc.9 (1983), 129–206.

    Article  MATH  MathSciNet  Google Scholar 

  2. C. L. Fefferman and D. H. Phong,On positivity of pseudo-differential operators, Proc. Natl. Acad. Sci. USA75 (1978), 4673–4674.

    Article  MATH  MathSciNet  Google Scholar 

  3. C. L. Fefferman and D. H. Phong,The uncertainty principle and sharp Gårding inequalities, Comm. Pure Appl. Math.34 (1981), 285–331.

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  5. L. Hörmander,The Analysis of Linear Partial Differential Operators, I-II-III-IV, Springer-Verlag, Berlin, 1983-1985.

    Google Scholar 

  6. A. Melin,Lower bounds for pseudo-differential operators, Arkiv för Matematik9 (1971), 117–140.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

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

    Cesare Parenti & Alberto Parmeggiani

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  1. Cesare Parenti
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  2. Alberto Parmeggiani
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Additional information

An erratum to this article is available at http://dx.doi.org/10.1007/BF02788035.

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Parenti, C., Parmeggiani, A. A necessary and sufficient condition for a lower bound for fourth-order pseudodifferential operators. J. Anal. Math. 69, 55–65 (1996). https://doi.org/10.1007/BF02787101

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  • DOI: https://doi.org/10.1007/BF02787101

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