Sobolev Problems with Spherical Mean Conditions and Traces of Quantized Canonical Transformations

We consider Sobolev problems (problems for an elliptic operator on a closed manifold with conditions on a closed submanifold) for the case in which these conditions are of nonlocal nature and include weighted spherical means of the unknown function over spheres of a given radius. For such problems, we establish a criterion for the Fredholm property and, in some special cases, obtain index formulas. © 2019, Pleiades Publishing, Ltd.