Hovhannes Khudaverdian

Operator pencils on densities

Let \Delta be a linear differential operator acting on the space of densities of a given weight t_0 on a manifold M. One can consider lifting of this operator, a pencil of operators {\Delta_t} passing through the operator \Delta such that any \Delta_t is a linear differential operator acting on
densities of weight $t$.
We study liftings which are equivariant with respect to group
of diffeomorphisms of $M$, and some of its subgroups.
Our analysis is essentially based on the simple but very important facts that
a pencil of operators can be identified with a linear differential operator \hat\Delta acting on the algebra of densities of all weights, and this algebra possesses a canonical scalar product.

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