NORMAL DIFFERENTIAL OPERATORS OF THIRD-ORDER

In the Hilbert space of vector-functions L-2(H, (a, b)), where H is any separable Hilbert space, the general representation in terms of boundary values of all normal extensions of the formally normal minimal operator, generated by linear differential-operator expressions of third order in the form l(u) = (u)''' (t) + A(3)u(t), A : D(A) subset of H -> H, A = A* >= E, is obtained in the first part of this study. Then, some spectral properties of these normal extensions are investigated. In particular, the case of A(-1) is an element of G(infinity)(H), asymptotic estimates of normal extensions of eigenvalues has been established at infinity.