Holomorphic operator semigroups with strong degeneration

In the work strongly holomorphic semigroups of the Sobolev type equation $L\dot u(t)=Mu(t)$ in a locally convex space degenerating on chains of $M$-adjoint vectors of operator $M$ of arbitrary length are constructed. It is the case of degenerate semigroups with more “wide” kernel than in the case of $(L,p)$-sectorial operator $M$. The example of an equation having resolving semigroup with strong degeneration is found.