On Semiclassical Asymptotics for Nonlocal Equations

We consider semiclassical operators equal to linear combinations of quantized canonical transformations with pseudodifferential operators as coefficients and study semiclassical asymptotics of the solutions of the corresponding equations. Under the assumption that the group of canonical transformations is finite, we reduce our problem to a similar problem for a matrix semiclassical pseudodifferential operator. The latter problem can be treated by standard methods. DOI 10.1134/S1061920822040136