We investigate the analytic perturbation of generalized inverses. Firstly we analyze the analytic perturbation of the Drazin generalized inverse (also known as reduced resolvent in operator theory). Our approach is based on spectral theory of linear operators as well as on a new notion of group reduced resolvent. It allows us to treat regular and singular perturbations in a unified framework. W...

In this paper, we introduce and study a generalized Yosida approximation operator associated to H(·, ·)-co-accretive operator and discuss some of its properties. Using the concept of graph convergence and resolvent operator, we establish the convergence for generalized Yosida approximation operator. Also, we show an equivalence between graph convergence for H(·, ·)-co-accretive operator and gen...

In this paper, we analyze the abstract degenerate Volterra integro-differential equations in sequentially complete locally convex spaces by using multivalued linear operators and vector-valued Laplace transform. We follow method which is based on use of (a, k)-regularized C-resolvent families generated suggests a very general way approaching equations. Among many other themes, consider Hille-Yo...

In this paper, we provide variation of constants formulae for linear (forward) stochastic Volterra integral equations (SVIEs, short) and Type-II backward (BSVIEs, in the usual Itô's framework. For these purposes, define suitable classes kernels introduce new notions products adapted L2-processes. Observing algebraic properties products, obtain by means corresponding resolvent. Our framework inc...

We consider the linear thermoelastic plate equations with free boundary conditions in the Lp in time and Lq in space setting. We obtain unique solvability with optimal regularity for the inhomogeneous problem in a uniform C-domain, which includes the cases of a bounded domain and of an exterior domain with C-boundary. Moreover, we prove uniform a priori-estimates for the solution. The proof is ...

We consider the 3-dimensional formulation of Einstein’s theory for spacetimes possessing a non-null Killing field ξ. It is known that for the vacuum case some of the basic field equations are deducible from the others. It will be shown here how this result can be generalized for the case of essentially arbitrary matter fields. The systematic study of the structure of the fundamental field equat...

We discuss recent progress in understanding the effects of certain trapping geometries on cut-off resolvent estimates, and thus on the qualititative behavior of linear evolution equations. We focus on trapping that is unstable, so that strong resolvent estimates hold on the real axis, and large resonance-free regions can be shown to exist beyond it.

We investigate analytic perturbations of the reduced resolvent of a nite-dimensional linear operator (also known as Drazin inverse in the linear algebra literature). Our approach is based on spectral theory of linear operators as well as on a new notion of group reduced resolvent. It allows to treat regular and singular perturbations in a uniied framework. We provide an algorithm for computing ...

Suppose that λ − T is left-invertible in L(H) for all λ ∈ Ω, where Ω is an open subset of the complex plane. Then an operator-valued function L(λ) is a left resolvent of T in Ω if and only if T has an extension T̃ , the resolvent of which is a dilation of L(λ) of a particular form. Generalized resolvents exist on every open set U , with U included in the regular domain of T . This implies a form...