He defended his Doktor nauk thesis in St. Petersburg Department of Steklov Institute of Mathematics of Russian Academy of Sciences in 1982.
In particular he discovered a necessary (later proven to be sufficient) condition for Cauchy problem to be well-posed no matter what the lower terms in the equation are.
[5] In a series of papers he explored propagation of singularities of symmetric hyperbolic systems inside of the domain and near the boundary.
His work in propagation of singularities logically guided him to the theory of asymptotic distribution of eigenvalues (a subject he has been studying ever since).
He again was invited give a talk at ICM—1986, Berkeley but again was not granted an exit visa by the Soviet authorities.