Traces of Quantized Canonical Transformations on Submanifolds and Their Applications to Sobolev Problems with Nonlocal Conditions

The paper presents conditions under which the traces of quantized canonical transformations on a submanifold are themselves quantized canonical transformations. The corresponding result is applied to certain nonlocal Sobolev problems in which the boundary conditions include quantized canonical transformations. © 2019, Pleiades Publishing, Ltd.