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 ...

Abstract. We analyze the behavior of the trace of the resolvent of an elliptic cone differential operator as the spectral parameter tends to infinity. The resolvent splits into two components, one associated with the minimal extension of the operator, and another, of finite rank, depending on the particular choice of domain. We give a full asymptotic expansion of the first component and expand ...

—The aim of this work is twofold : a) it uses the fundamental matrix of the resolvent of a regular pencil in order to provide an algorithm for the computation of the fundamental matrix of the resolvent of a polynomial matrix, and b) it proposes a closed formula for the forward, backward and symmetric solution of an AutoRegressive Moving Average (ARMA). This closed formula is represented in term...

We will determine the number of powers of α that appear with nonzero coefficient in an α-power linear differential resolvent of smallest possible order of a univariate polynomial P(t) whose coefficients lie in an ordinary differential field and whose distinct roots are differentially independent over constants. We will then give an upper bound on the weight of an α-resolvent of smallest possibl...

We present results concerning resolvent estimates for the linear operator associated with the system of differential equations governing 2 dimensional perturbations of plane Couette flow. We prove estimates on the L2 norm of the resolvent of this operator showing this norm to be proportional to the Reynolds number R for a region of the unstable half plane. For the remaining region, we show that...

Having as start point the classic definitions of resolvent set and spectrum of a linear bounded operator on a Banach space, we introduce the resolvent set and spectrum of a family of linear bounded operators on a Banach space. In addition, we present some results which adapt to asymptotic case the classic results.

We study nonsymmetric tridiagonal operators acting in the Hilbert space l and describe the spectrum and the resolvent set of such operators in terms of a continued fraction related to the resolvent. In this way we establish a connection between Padé approximants and spectral properties of nonsymmetric tridiagonal operators.

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.