Related papers: On the ascent-descent spectrum

We carry the index theory for manifolds with boundary of B\"ar and Ballmann over to first order differential operators on metric graphs. This approach results in a short proof for the index of such operators. Then the self-adjoint…

In this paper, we introduce and study a new class of bounded linear operators on complex Hilbert spaces, which we call 2-C-normal operators. This class is inspired by and closely related to the notion of 2-normal operators, with additional…

For a given self-adjoint operator $A$ with discrete spectrum, we completely characterize possible eigenvalues of its rank-one perturbations~$B$ and discuss the inverse problem of reconstructing $B$ from its spectrum.

We give upper and lower bounds on the spectral radius of a graph in terms of the number of walks. We generalize a number of known results.

For nonautonomous linear difference equations, we introduce the notion of the so-called nonuniform dichotomy spectrum and prove a spectral theorem. Moreover, we introduce the notion of weak kinematical similarity and prove a reducibility…

We review the basic properties of paired operators and their adjoints, the transposed paired operators, with particular reference to commutation relations, and we study the properties of their kernels, bringing out their similarities and…

We present methods for obtaining new solutions to the bispectral problem. We achieve this by giving its abstract algebraic version suitable for generalizations. All methods are illustrated by new classes of bispectral operators.

Tensors are multiway arrays of data, and transverse operators are the operators that change the frame of reference. We develop the spectral theory of transverse tensor operators and apply it to problems closely related to classifying…

This paper delves into several characterizations of $A$-approximate point spectrum of A-bounded operators acting on a complex semi-Hilbertian space $H$ and also investigates properties of the $A$-approximate point spectrum for the tensor…

In this paper, we introduce and study the spectral property $(E_A)$. This property means that the difference between the approximate point spectrum and the upper semi-Fredholm spectrum coincides with the difference between the approximate…

We investigate the spectral properties of balanced trees and dendrimers, with a view toward unifying and improving the existing results. Here we find a semi-factorized formula for their characteristic polynomials. Afterwards, we determine…

Lecture notes for one of the courses at the OPSFA Summerschool 6, July 11-15, 2016. All the results in these notes have appeared in the literature. Many special functions are eigenfunctions to explicit operators, such as difference and…

We consider the topological relation behind the spectral behavior of a linear operator that arises in the stability problem of traveling waves on a large bounded domain. When the domain size tends to infinity, the absolute and asymptotic…

Covering ill-posed problems with compact and non-compact operators regarding the degree of ill-posedness is a never ending story written by many authors in the inverse problems literature. This paper tries to add a new narrative and some…

We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless,…

Spectra of the second derivative operators corresponding to the special PT-symmetric point interactions are studied. The results are partly the completion of those obtained in [1]. The particular PT-symmetric point interactions causing…

We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or infinitely many spectral gaps along with corresponding…

We show the linear convergence of Dykstra's algorithm for sets intersecting in a manner slightly stronger than the usual constraint qualifications.

In the scattering theory framework, we point out a connection between the spectrum of the scattering matrix of two operators and the spectrum of the difference of spectral projections of these operators.

Nonlinear spectral graph theory is an extension of the traditional (linear) spectral graph theory and studies relationships between spectral properties of nonlinear operators defined on a graph and topological properties of the graph…