On the conicity of eigenvalues intersections for parameter-dependent self-adjoint operators

On Eigenvalues Problem for Self-adjoint Operators with Singular Perturbations

We investigate the eigengenvalues problem for self-adjoint operators with the singular perturbations. The general results presented here include weakly as well as strongly singular cases. We illustrate these results on two models which correspond to so-called additive strongly singular perturbations.

Local two-sided bounds for eigenvalues of self-adjoint operators

We examine the equivalence between an extension of the Lehmann-Maehly-Goerisch method developed a few years ago by Zimmermann and Mertins, and a geometrically motivated method developed more recently by Davies and Plum. We establish a general framework which allows sharpening various previously known results in these two settings and determine explicit convergence estimates for both methods. We...

Non-variational Approximation of Discrete Eigenvalues of Self-adjoint Operators

We establish sufficiency conditions in order to achieve approximation to discrete eigenvalues of self-adjoint operators in the second-order projection method suggested recently by Levitin and Shargorodsky, [15]. We find explicit estimates for the eigenvalue error and study in detail two concrete model examples. Our results show that, unlike the majority of the standard methods, second-order pro...

A strategy for detecting extreme eigenvalues bounding gaps in the discrete spectrum of self-adjoint operators

For a self-adjoint linear operator with discrete spectrum or a Hermitian matrix the “extreme” eigenvalues define the boundaries of clusters in the spectrum of real eigenvalues. The outer extreme ones are the largest and the smallest eigenvalues. If there are extended intervals in the spectrum in which no eigenvalues are present, the eigenvalues bounding these gaps are the inner extreme eigenval...

On Families of Self Adjoint Operators