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On the index of pseudodifferential operators with isolated singularities in the symbols. (Russian) Zbl 0722.35096
Elliptic pseudodifferential operators on compact manifolds without edges and with a finite number of conical points are considered. Isolated singularities of the symbols must satisfy the following requirement: there exists lim $$a_ 0(x,\xi)$$ with respect to any direction, when x approaches the singularity $$x^ 0$$. The goal of the investigations is to express the index of a pseudodifferential operator in terms of its symbol. A formula for the index is presented that generalizes the corresponding formula obtained by B. Fedosov and L. Hörmander in the analytic case.

##### MSC:
 35S05 Pseudodifferential operators as generalizations of partial differential operators
##### Keywords:
singularities of the symbols; index