As a step toward understanding the analytic behavior of TypeIII Ricci flow singularities, i.e. immortal solutions that exhibit |Rm | ≤ C/t curvature decay, we examine the linearization of an equivalent flow at certain fixed points discovered recently by Baird–Danielo and Lott: non-gradient homogeneous Ricci solitons on nilpotent Lie groups. We show that the linearized operators at these fixed p...

The paper deals with semigroups of operators associated with delay differential equation: ẋ(t) = Ax(t) + L1x(t− h) + L2xt, where A is the infinitesimal generator of an analytic semigroup on a Hilbert space X and L1, L2 are densely defined closed operators in X and L2(−h, 0;X) respectively. The adjoint semigroup of the solution semigroup of the delay differential equation is characterized. Eigen...

The paper deals with semigroups of operators associated with delay diierential equation: _ x(t) = Ax(t) + L 1 x(t ? h) + L 2 xt; where A is the innnitesimal generator of an analytic semigroup on a Hilbert space X and L 1 , L 2 are densely deened closed operators in X and L 2 (?h; 0;X) respectively. The adjoint semigroupof the solution semigroupof the delay diierentialequation is characterized. ...

We consider the dynamics of expanding semigroups generated by finitely many rational maps on the Riemann sphere. We show that for an analytic family of such semigroups, the Bowen parameter function is real-analytic and plurisubharmonic. Combining this with a result obtained by the first author, we show that if for each semigroup of such an analytic family of expanding semigroups satisfies the o...

Nuclearity of the Hankel operator is a known sufficient condition for convergence of Lyapunov-balanced truncations. We show how a previous result on nuclearity of Hankel operators of systems with an analytic semigroup can be extended to systems with a semigroup of class D with p ≥ 1 (the case p = 1 being the analytic case). For semigroups that are generated by a Dunford-Schwartz spectral operat...