Abstract— We consider the inversion of perturbed linear operators on Hilbert space. Namely, we study linear operators that depend on a small parameter and are singular when the parameter is equal to zero. First we consider the af£ne dependence on the parameter. We treat subsequently the cases of bounded operators with closed range, bounded operators with non closed range, and densely de£ned and...

The known definition of an analytic n-times integrated semigroup is reconsidered and one superfluous condition is removed. It is proved that every densely defined generator of an exponentially bounded, analytic n-times integrated semigroup of angle α with the appropriate growth rate at zero is also the generator of an analytic C0-semigroup of the same angle. AMS Mathematics Subject Classificati...

We extend the concept of intrinsic ultracontractivity to non-symmetric semigroups and prove the intrinsic ultracontractivity of the Dirichlet semigroups of nonsymmetric second order elliptic operators in bounded Lipschitz domains.

The paper deals with a homogenization problem for a nonlocal linear operator with a kernel of convolution type in a medium with a periodic structure. We consider the natural diffusive scaling of this operator and study the limit behavior of the rescaled operators as the scaling parameter tends to 0. More precisely we show that in the topology of resolvent convergence the family of rescaled oper...

Abstract This paper is devoted to studying the linear system of partial differential equations modelling a one-dimensional thermo-porous-elastic problem with microtemperatures in context dual-phase-lag heat conduction. Existence, uniqueness, and exponential decay solutions are proved. Polynomial stability also obtained case that relaxation parameters satisfy certain equality. Our arguments base...