On the index of elliptic translators

Researchers conducted a study to calculate the index of elliptic translators and apply it to obtain an index formula for the Sobolev problem on a manifold with singularities. A pseudodifferential translator from the function space on the manifold Yq to the function space on the manifold Y p was defined as the composition of a co-boundary operator on Y q and a boundary operator on Yp. The elliptic theory was constructed for operators of the form (4) in the multidimensional case where the submanifold X had positive dimension. It was also shown that all operators in the expression 8 were infinitely smoothing outside the submanifold X except the identity operator.