The self-adjoint solution of Lyapunov’s equation of \(C\)-semigroups and stability. (Chinese. English summary) Zbl 1174.47039
Summary: In this paper, we discuss selfadjoint solutions of the Lyapunov equation of \(C\)-semigroups in Hilbert space, extending a theorem of Lyapunov. Moreover, a sufficient condition for a selfadjoint solution of asymptotic stability is obtained and a sharper upper bound of asymptotically stable \(C\)-semigroups is given.
MSC:
47D60 | \(C\)-semigroups, regularized semigroups |
34K25 | Asymptotic theory of functional-differential equations |