The present paper considers the operator pencil A ( λ ) = 0 + 1 , where ≠ are bounded linear mappings between complex Hilbert spaces and is neither one-to-one nor onto. Assuming that an isolated singularity of image closed, certain operators defined recursively starting from they shown to provide a characterization null space in principal part resolvent logarithmic residues at 0. relations with...

What is known today as the Lee-Friedrichs model is characterized by a self-adjoint operator H on a Hilbert space H, which is the sum of two self-adjoint operators H0 and V , such that H,H0 and V have common domain; H0 has absolutely continuous spectrum (of uniform multiplicity) except for the end-point of the semi-bounded from below spectrum, and one or more eigenvalues which may or may not be ...

Abstract: The classical Weyl-von Neumann theorem states that for any selfadjoint operator A in a separable Hilbert space H there exists a (non-unique) Hilbert-Schmidt operator C = C∗ such that the perturbed operator A + C has purely point spectrum. We are interesting whether this result remains valid for non-additive perturbations by considering self-adjoint extensions of a given densely define...

The equations for the electromagnetic field in an anisotropic media are written in a form containing only the transverse field components relative to a half plane boundary. The operator corresponding to this formulation is the electromagnetic system’s matrix. A constructive proof of the existence of directional wave-field decomposition with respect to the normal of the boundary is presented. In...

Let A be a bounded operator on a Banach space X. A scalar λ is in the spectrum of A if the operator A − λ is not invertible. Case closed. What more is there to say? As anyone with the slightest exposure to operator theory will testify, there is so much out there that no book could come close to being comprehensive. What authors do in such situations is choose a small area or topic of interest t...

For selfadjoint elliptic operators in divergence form with ?-periodic coefficients of even order 2m ? 4 we approximate the resolvent energy operator norm $$ {\left\Vert \bullet \right\Vert}_{L^2\to {H}^m} a remainder ?2 as ? ? 0.

A singularly perturbed second order elliptic system in the entire space is treated. The coefficients of the systems oscillate rapidly and depend on both slow and fast variables. The homogenized operator is obtained and, in the uniform norm sense, the leading terms of the asymptotic expansion are constructed for the resolvent of the operator described by the system. The convergence of the spectr...

In previous papers the arithmetic of hierarchical matrices has been described, which allows to compute the inverse, for instance, of finite element stiffness matrices discretising an elliptic operator L. The required computing time is up to logarithmic factors linear in the dimension of the matrix. In particular, this technique can be used for the computation of the discrete analogue of a resol...

This article investigates the approximate controllability of second order non-autonomous functional evolution equations involving non-instantaneous impulses and nonlocal conditions. First, we discuss linear system in detail, which lacks existing literature. Then, derive sufficient conditions for our separable reflexive Banach spaces via operator, resolvent operator conditions, Schauder’s fixed ...

Let AN be the symmetric operator given by the restriction of A toN , where A is a self-adjoint operator on the Hilbert space H and N is a linear dense set which is closed with respect to the graph norm on D(A), the operator domain of A. We show that any self-adjoint extension AΘ of AN such that D(AΘ)∩D(A) = N can be additively decomposed by the sum AΘ = Ā + TΘ, where both the operators Ā and TΘ...