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ISAAC Congress (International Society for Analysis, its Applications and Computation)

ISAAC 2017: Mathematical Analysis and Applications—Plenary Lectures pp 109–137Cite as

Almost-Positivity Estimates of Pseudodifferential Operators

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 262))

Abstract

In this paper I will give a survey on a priori estimates such as the Gårding, Sharp-Gårding, Melin, Hörmander and the Fefferman–Phong inequalities for pseudodifferential operators, discuss some generalizations and open problems in some directions. Finally, I will describe what is known at present in the case of systems of pseudodifferential operators, the latter being a still largely open and unexplored area.

I wish to thank the organizers of the ISAAC conference 2017 held in Växjö (Sweden), and in particular Luigi Rodino and Joachim Toft

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Authors and Affiliations

  1. Department of Mathematics, University of Bologna, Piazza di Porta San Donato 5, 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 Torino, Turin, Italy

    Luigi G. Rodino

  2. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Joachim Toft

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Parmeggiani, A. (2018). Almost-Positivity Estimates of Pseudodifferential Operators. In: Rodino, L., Toft, J. (eds) Mathematical Analysis and Applications—Plenary Lectures. ISAAC 2017. Springer Proceedings in Mathematics & Statistics, vol 262. Springer, Cham. https://doi.org/10.1007/978-3-030-00874-1_4

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