Communications in Mathematical Physics

, Volume 333, Issue 3, pp 1585–1615 | Cite as

Green-Hyperbolic Operators on Globally Hyperbolic Spacetimes

  • Christian Bär


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.


Cauchy Problem Vector Bundle Wave Operator Principal Symbol Lorentzian Manifold 
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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institut für MathematikUniversität PotsdamPotsdamGermany

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