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Jun 24, 2018 at 23:53 comment added truebaran Not quite the space of symbols: obviously the idea is to call by a ,,symbol'' objects which take into account only the highest order term of a differential operator but genuine symbol are sections over $T^*M$ of the bundle $Hom(E,F)$. The paper which you mention is interesting but I don't see how it provides the answer (for example the last Proposition in zeroth section is without proof).
Jun 23, 2018 at 16:02 history answered Peter Michor CC BY-SA 4.0