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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.

35S05 Pseudodifferential operators as generalizations of partial differential operators