On the resolvent existence and the separability of a hyperbolic operator with fast growing coefficients in L2(R2)

This paper studies the question of resolvent existence, as well as, smoothness elements from definition domain (separability) a class hyperbolic differential operators defined in an unbounded with greatly increasing coefficients after closure space L2(R2). Such problem was previously put forward by I.M. Gelfand for elliptic operators. Here, we note that detailed analysis shows when studying spectral properties specified domain, behavior at infinity plays important role.