Related papers: On G-convergence of positive Self-adjoint operator…

This chapter deals with the notion of the resolvent of a self-adjoint operator. We pay special attention to the convergence of unbounded self-adjoint operators in several resolvent senses, and how they are related to the convergence of…

In this paper we investigate homogenization results for the principal eigenvalue problem associated to $1$-homogeneous, uniformly elliptic, second-order operators. Under rather general assumptions, we prove that the principal eigenpair…

We consider the linear Dirac operator with a (-1)-homogeneous locally periodic potential that varies with respect to a small parameter. Using the notation of G-convergence for positive self-adjoint operators in Hilbert spaces we prove…

We consider sequences of elliptic and parabolic operators in divergence form and depending on a family of vector fields. We show compactness results with respect to G-convergence, or H-convergence, by means of the compensated compactness…

The convergence of the so-called quadratic method for computing eigenvalue enclosures of general self-adjoint operators is examined. Explicit asymptotic bounds for convergence to isolated eigenvalues are found. These bounds turn out to…

We describe the spectrum of a non-self-adjoint elliptic system on a finite interval. Under certain conditions we find that the eigenvalues form a discrete set and converge asymptotically at infinity to one of several straight lines. The…

In this paper following the same methods in [M. Kadakal, O. Sh. Mukhtarov, Sturm-Liouville problems with discontinuities at two points, Comput. Math. Appl., 54 (2007) 1367-1379] we investigate discontinuous two-point boundary value problems…

Given a self-adjoint involution J on a Hilbert space H, we consider a J-self-adjoint operator L=A+V on H where A is a possibly unbounded self-adjoint operator commuting with J and V a bounded J-self-adjoint operator anti-commuting with J.…

We consider an elliptic operator in which the second-order term is very small in one direction. In this regime, we study the behaviour of the principal eigenfunction and of the principal eigenvalue. Our first result deals with the limit of…

A lower semi-definite self-adjoint linear operator in a Hilbert space is taken whose discrete spectrum is not empty and comprises at least several eigenvalues $\lambda_{min}=\lambda_1\leqslant\ldots\leqslant\lambda_m<\sigma_{ess}$. The…

For a class of non-selfadjoint $h$--pseudodifferential operators with double characteristics, we give a precise description of the spectrum and establish accurate semiclassical resolvent estimates in a neighborhood of the origin.…

In this work we study the homogenization problem for (nonlinear) eigenvalues of quasilinear elliptic operators. We prove convergence of the first and second eigenvalues and, in the case where the operator is independent of $\varepsilon$,…

We prove inclusion theorems for both spectra and essential spectra as well as two-sided bounds for isolated eigenvalues for Klein-Gordon type Hamiltonian operators. We first study operators of the form $JG$, where $J$, $G$ are selfadjoint…

In this brief note we describe relations between the well known notion of a relatively bounded operator and the operator E-norms considered in [arXiv:1806.05668]. We show that the set of all $\sqrt{G}$-bounded operators equipped with the…

The abstract theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of a second-order elliptic operator on $\mathbb{R}^{n}$ with linear boundary conditions on (a relatively open part of) a…

Maximization and minimization problems of the principle eigenvalue for divergence form second order elliptic operators with the Dirichlet boundary condition are considered. The principal eigen map of such elliptic operators is introduced…

A concrete formulation of the Lehmann-Maehly-Goerisch method for semi-definite self-adjoint operators with compact resolvent is considered. Precise rates of convergence are determined in terms of how well the trial spaces capture the…

The main result (roughly) is that if (H_i) converges weakly to H and if also f(H_i) converges weakly to f(H), for a single strictly convex continuous function f, then (H_i) must converge strongly to H. One application is that if f(pr(H)) =…

The general self-adjoint elliptic boundary value problems are considered in a domain $G\subset \Bbb R^{n+1}$ with finitely many cylindrical ends. The coefficients are stabilizing (as $x\to\infty$, $x\in G$) so slowly that we can only…

We formulate, for any Lie group G acting isometrically on a manifold M, the general notion of a G-equivariant elliptic operator that is invertible outside of a G-cocompact subset of M. We prove a version of the Rellich lemma for this…