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Green-Hyperbolic Operators on Globally Hyperbolic Spacetimes

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Abstract

Green-hyperbolic operators are linear differential operators acting on sections of a vector bundle over a Lorentzian manifold which possess advanced and retarded Green’s operators. The most prominent examples are wave operators and Dirac-type operators. This paper is devoted to a systematic study of this class of differential operators. For instance, we show that this class is closed under taking restrictions to suitable subregions of the manifold, under composition, under taking “square roots”, and under the direct sum construction. Symmetric hyperbolic systems are studied in detail.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Potsdam, Am Neuen Palais 10, 14469, Potsdam, Germany

    Christian Bär

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  1. Christian Bär
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Correspondence to Christian Bär.

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Communicated by P. T. Chruściel

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Bär, C. Green-Hyperbolic Operators on Globally Hyperbolic Spacetimes. Commun. Math. Phys. 333, 1585–1615 (2015). https://doi.org/10.1007/s00220-014-2097-7

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  • DOI: https://doi.org/10.1007/s00220-014-2097-7

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