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Studies in Phase Space Analysis with Applications to PDEs pp 313–335Cite as

Birkhäuser

On the Problem of Positivity of Pseudodifferential Systems

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Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 84))

Abstract

I will give here in the first place a survey of the problem of positivity estimates for systems of ψdos, such as the Sharp-Gårding and the Fefferman–Phong inequalities. Next, I will generalize Fujiwara’s construction of the approximate positive/negative part of a first-order scalar ψdo to certain 2 ×2 systems of first-order ψdos.

2010 Mathematics Subject Classification: Primary: 35S05; Secondary: 35B45, 35A30.

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Acknowledgements

I wish to thank the organizers of the conference, Massimo Cicognani, Ferruccio Colombini, and Daniele Del Santo, for the great work they have done in the organization of the workshop. I wish also to thank Sandro Coriasco for the very useful remarks.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, I-40126, Bologna, Italy

    Alberto Parmeggiani

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  1. Alberto Parmeggiani
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Correspondence to Alberto Parmeggiani .

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Editors and Affiliations

  1. , Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato, 5, Bologna, I-40126, Italy

    Massimo Cicognani

  2. , Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo, 5, Pisa, I-56127, Italy

    Ferruccio Colombini

  3. , Dipartimento di Matematica e Geoscienze, Università di Trieste, Via Valerio, 12/1 12/1, Trieste, I-34127, Italy

    Daniele Del Santo

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Parmeggiani, A. (2013). On the Problem of Positivity of Pseudodifferential Systems. In: Cicognani, M., Colombini, F., Del Santo, D. (eds) Studies in Phase Space Analysis with Applications to PDEs. Progress in Nonlinear Differential Equations and Their Applications, vol 84. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-6348-1_14

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